{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ADKY4re5Kx-5"
      },
      "source": [
        "##### Copyright 2019 The TensorFlow Probability Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "S2AOrHzjK0_L"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "56dF5DnkKx0a"
      },
      "source": [
        "# Approximate inference for STS models with non-Gaussian observations\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/STS_approximate_inference_for_models_with_non_Gaussian_observations\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/STS_approximate_inference_for_models_with_non_Gaussian_observations.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/STS_approximate_inference_for_models_with_non_Gaussian_observations.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/STS_approximate_inference_for_models_with_non_Gaussian_observations.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "laPe5xoS42ob"
      },
      "source": [
        "This notebook demonstrates the use of TFP approximate inference tools to incorporate a (non-Gaussian) observation model when fitting and forecasting with structural time series (STS) models. In this example, we'll use a Poisson observation model to work with discrete count data."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4YJz-JDu0X9E"
      },
      "outputs": [],
      "source": [
        "import time\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "import tensorflow.compat.v2 as tf\n",
        "import tensorflow_probability as tfp\n",
        "\n",
        "from tensorflow_probability import bijectors as tfb\n",
        "from tensorflow_probability import distributions as tfd\n",
        "\n",
        "tf.enable_v2_behavior()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YagBskFAO34k"
      },
      "source": [
        "## Synthetic Data\n",
        "\n",
        "First we'll generate some synthetic count data:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OKgRbodJ4EuU"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x271692e70d90>]"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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Bvli3cir0BpZ69AlnyeXyQXl1pGQPWJDwKyoqsGvXLtTX1+PZZ5/F8uXLB74y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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x271690e94c90>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "num_timesteps = 30\n",
        "observed_counts = np.round(3 + np.random.lognormal(np.log(np.linspace(\n",
        "    num_timesteps, 5, num=num_timesteps)), 0.20, size=num_timesteps)) \n",
        "observed_counts = observed_counts.astype(np.float32)\n",
        "plt.plot(observed_counts)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OH2nvBuOxDrd"
      },
      "source": [
        "## Model\n",
        "\n",
        "We'll specify a simple model with a randomly walking linear trend:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hSsekKzIwsg6"
      },
      "outputs": [],
      "source": [
        "def build_model(approximate_unconstrained_rates):\n",
        "  trend = tfp.sts.LocalLinearTrend(\n",
        "      observed_time_series=approximate_unconstrained_rates)\n",
        "  return tfp.sts.Sum([trend],\n",
        "                     observed_time_series=approximate_unconstrained_rates)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iY-pH3hQz0Vp"
      },
      "source": [
        "Instead of operating on the observed time series, this model will operate on the series of Poisson rate parameters that govern the observations.\n",
        "\n",
        "Since Poisson rates must be positive, we'll use a bijector to transform the\n",
        "real-valued STS model into a distribution over positive values. The `Softplus`\n",
        "transformation $y = \\log(1 + \\exp(x))$ is a natural choice, since it is nearly linear for positive values, but other choices such as `Exp` (which transforms the normal random walk into a lognormal random walk) are also possible."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Hg_B4tofzxgc"
      },
      "outputs": [],
      "source": [
        "positive_bijector = tfb.Softplus()  # Or tfb.Exp()\n",
        "\n",
        "# Approximate the unconstrained Poisson rate just to set heuristic priors.\n",
        "# We could avoid this by passing explicit priors on all model params.\n",
        "approximate_unconstrained_rates = positive_bijector.inverse(\n",
        "    tf.convert_to_tensor(observed_counts) + 0.01)\n",
        "sts_model = build_model(approximate_unconstrained_rates)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Pxua5B2wxIMz"
      },
      "source": [
        "To use approximate inference for a non-Gaussian observation model,\n",
        "we'll encode the STS model as a TFP JointDistribution. The random variables in this joint distribution are the parameters of the STS model, the time series of latent Poisson rates, and the observed counts.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vquh2LxgBjfy"
      },
      "outputs": [],
      "source": [
        "Root = tfd.JointDistributionCoroutine.Root\n",
        "def sts_with_poisson_likelihood_model():\n",
        "  # Encode the parameters of the STS model as random variables.\n",
        "  param_vals = []\n",
        "  for param in sts_model.parameters:\n",
        "    param_val = yield Root(param.prior)\n",
        "    param_vals.append(param_val)\n",
        "\n",
        "  # Use the STS model to encode the log- (or inverse-softplus)\n",
        "  # rate of a Poisson.\n",
        "  unconstrained_rate = yield sts_model.make_state_space_model(\n",
        "      num_timesteps, param_vals)\n",
        "  rate = positive_bijector.forward(unconstrained_rate[..., 0])\n",
        "  observed_counts = yield tfd.Independent(tfd.Poisson(rate),\n",
        "      reinterpreted_batch_ndims=1)\n",
        "model = tfd.JointDistributionCoroutine(sts_with_poisson_likelihood_model)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R-3amgmKhYn1"
      },
      "source": [
        "### Preparation for inference\n",
        "\n",
        "We want to infer the unobserved quantities in the model, given the observed counts. First, we condition the joint log density on the observed counts."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rSj7blvWh1w8"
      },
      "outputs": [],
      "source": [
        "# Condition a joint log-prob on the observed counts.\n",
        "target_log_prob_fn = lambda *args: model.log_prob(args + (observed_counts,))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RFeZ7NYt1qnw"
      },
      "source": [
        "HMC and VI inference also like to operate over unconstrained real-valued spaces, so we'll construct the list of bijectors that constrains each of the parameters to their respective supports."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Dyhb06i41qIg"
      },
      "outputs": [],
      "source": [
        "constraining_bijectors = ([param.bijector for param in sts_model.parameters] +\n",
        "                           # `unconstrained_rate` is already unconstrained, but\n",
        "                           # we can speed up inference by rescaling it.\n",
        "                           [tfb.Scale(positive_bijector.inverse(\n",
        "                               np.float32(np.max(observed_counts / 5.))))])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "25nJYyx-nW2T"
      },
      "source": [
        "## Inference with HMC\n",
        "\n",
        "We'll use HMC (specifically, NUTS) to sample from the joint posterior over model parameters and latent rates.\n",
        "\n",
        "This will be significantly slower than fitting a standard STS model with HMC, since in addition to the model's (relatively small number of) parameters we also have to infer the entire series of Poisson rates. So we'll run for a relatively small number of steps; for applications where inference quality is critical it might make sense to increase these values or to run multiple chains."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NMPlVBk6PcpT"
      },
      "outputs": [],
      "source": [
        "#@title Sampler configuration\n",
        "\n",
        "# Allow external control of sampling to reduce test runtimes.\n",
        "num_results = 100 # @param { isTemplate: true}\n",
        "num_results = int(num_results)\n",
        "\n",
        "num_burnin_steps = 50 # @param { isTemplate: true}\n",
        "num_burnin_steps = int(num_burnin_steps)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mhSe-GFDPg9o"
      },
      "source": [
        "First we specify a sampler, and then use `sample_chain` to run that sampling\n",
        "kernel to produce samples."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "15ue-mBGdcmh"
      },
      "outputs": [],
      "source": [
        "sampler = tfp.mcmc.TransformedTransitionKernel(\n",
        "    tfp.mcmc.NoUTurnSampler(\n",
        "        target_log_prob_fn=target_log_prob_fn,\n",
        "        step_size=0.1),\n",
        "    bijector=constraining_bijectors)\n",
        "\n",
        "adaptive_sampler = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
        "    inner_kernel=sampler,\n",
        "    num_adaptation_steps=int(0.8 * num_burnin_steps),\n",
        "    target_accept_prob=0.75,\n",
        "    # NUTS inside of a TTK requires custom getter/setter functions.\n",
        "    step_size_setter_fn=lambda pkr, new_step_size: pkr._replace(\n",
        "        inner_results=pkr.inner_results._replace(step_size=new_step_size)\n",
        "        ),\n",
        "    step_size_getter_fn=lambda pkr: pkr.inner_results.step_size,\n",
        "    log_accept_prob_getter_fn=lambda pkr: pkr.inner_results.log_accept_ratio,\n",
        ")\n",
        "\n",
        "initial_state = [b.forward(tf.random.normal(part_shape))\n",
        "                 for (b, part_shape) in zip(\n",
        "                     constraining_bijectors, model.event_shape[:-1])]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jvriVTPlih3B"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Inference ran in 53.57s.\n"
          ]
        }
      ],
      "source": [
        "# Speed up sampling by tracing with `tf.function`.\n",
        "@tf.function(autograph=False, experimental_compile=True)\n",
        "def do_sampling():\n",
        "  return tfp.mcmc.sample_chain(\n",
        "      kernel=adaptive_sampler,\n",
        "      current_state=initial_state,\n",
        "      num_results=num_results,\n",
        "      num_burnin_steps=num_burnin_steps)\n",
        "\n",
        "t0 = time.time()\n",
        "samples, kernel_results = do_sampling()\n",
        "t1 = time.time()\n",
        "print(\"Inference ran in {:.2f}s.\".format(t1-t0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FwE0yWm_2_kE"
      },
      "source": [
        "We can sanity-check the inference by examining the parameter traces. In this case they appear to have explored multiple explanations for the data, which is good, although more samples would be helpful to judge how well the chain is mixing."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LPOVTbboAtGr"
      },
      "outputs": [
        {
          "data": {
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GDRvW4OtWWFhYpzzJycnIysqS2u/atQvjx48HYLYcTZs2DT179oRCoUB6ejoA4PTp0w0+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\nY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m+fmcC7ZycQkVT8rzs35X0j0lzvwKUi9gz89uQYJmZCWNtdhzqXDXfcsAqbVjVCklWI\nPGd6n5MRed2zHQzL0JD7WPWTA9MIhCTzXNfTWQueY3D6kl5sB8KymfySLySjmwHMCbHVMNhmSRXb\nAPDe9a34l3/vw/khX94DGLLhiuX1ePXEKL7//GmcuTSL1gYHfHNRXLVu8RdWVuJ9m9sRCEk48Ktz\nuDDiR09Hacc3T8yE0Fxrx+ZVjXjhzUvobF5cEX6ZmAtLePXYKA73jWFVZy3uuGFVwk2lZIxrXyow\nDINP77oCl8YDOHZ+Go8/fxobVjbAYePwwhuX0bOsHssbnbCJHFRVS2mMnZoN4+lfn8eRc5MIRRSs\n6vRg701rsKoj83AMQE9TkGQ14/TIfPncxzdjcDyAwbEAfvabfjz8vTdxdW8zGjx2cCyDt89Mot5t\nw+qu+fev3DAMgw9e2Ykf//o8PnBlJ265qstUwO65dR0ujvrNAmlZixsnL3oxF5Zo43oSZPhWOYtt\nkgZSDhsJAKxf3gCnjTc91Ndv6cALb17CuaFXEZVVRCUViqLi7OUZ1NaIODU4A5Fnsaa7Dh++ZllC\nZnWutNQ58M6ZibTngnw4PzSLdd31+NNPbMnp52wCh/4RHz7/Ty+j3m3HX3/mPTmtVP325Bhq7LzZ\nm2QTOKxdVv//2jv36CjLO49/5p7JfRKSTC4kgSSCSYAAgYCiGMKiKDVgCwar7lY8tB6LWNvTZetp\n5Yi7nrjdpS3WCntW69YtLVUrhBURAUu5SKhRwAQQQmICucHkRhJym3n2j0kG0kwuTC7zBJ7POZzD\nvMzly/u+3/f9vb/n9/we12TTltaOfkd6B0N3r+0AP6Or45IqI5GQGbeF8bvdZ3jvQDENze0EjNAC\nDJPjLOz//CJHi6p58M54lt41kY5OOwb9zVuXKyvz06J4/6/nOXiiYuSD7YZWbo+zcNv4YIL8jUwa\npRuTt7hUf5W8QyV8WlhNe6eDyFBfPjpWzpnyetY8NMW1et+tVrMNMCfZypxkmJvcxAtv5vPegfNc\nbevkaNeEPWcQoaHT7mDKxFAWpscQGuhDeU0Tb390hk6HYPbkcCJD/didX8a//s9nLM9M4L7ZsX1m\nuS/X99/2z1MMeh0JUUEkRAUx87Ywfv/xV5wpr6ehqR27Q2DQa1l614Re5SUykEQexx0AABL9SURB\nVDUzhiw3LQ7npliZm3JtifgFM6P5752neOGNfJ64/3aSBygfuJUI9jfibzZQNoodWzrtXZntUXpI\nvy8jtsfrnKxEpiWGsutoGf6+RpbOi6e2oZXNeUU0X+3gkYVJzE+LGpZ7eliwD3aHoPZK65AflFta\nO7h4uZnZHqwVYgk00dnpYFJsMEWldeQX1TA39ZpHzpTVUVhaR2t7JyaDjrBgM6kTQggJ9KGs+grH\nTtVwd1pUj2OWmjCOd/ae5WpbJ81XO/EzDe1Btrvm2xJgwmxyTgSva3QfbIuuevUvzl7G7hDYHQ46\n7YI4awD3zo51+5mR4pYLts0mPTMmhfFpYTVhwT5kz5swIr8zKTbYOcwRFciSO+IBVKDtJcwmPemT\nwzl6qpqHs5J6TQoZiJLKRnxN+gGXlO7otFN/pY2wYDMGvZZ/f+oOdDdpK79utuQV8XVlI3NSIsic\nHkOcNYCCry7xX3lFvPNJMasfTAG6arZvocz29cSE+5M5PZp9BRcB+Ob8icxMjuSvn5eDcE5gOvJl\nFRu3HXd9Js4awPeyU4joysLOT4vizV2n+dP+Ymob2shZmIhOq+WzM5fYfayMlVlJTIgMdK08OtzB\n9vUE+hn5XnYq4NSugREvzxoN5iRbibD4snlHIT//wxfcHmdhcUYsk+MsvQI+hxBcqGniSksHWo2z\n84mpj0W2bgY0Gg2xEf6U1TSN2m92t830VhcjjUZDcnwIyfEhhIUFcOnSFSIsvuR+dy5a7fDez8O7\nsulfVzUxLsiMraGV48WXMRl0BPkbMRv1BPgaBlWXXFzhnMic2M8S8X2RsyCRb949ER+TnvVv5LPz\nSCkZyRFotRpOFNvY9O4JHEJg6moR6BACf7OBp5el8vZHX+Hva2DZXT3r1lMnhrLt4694+6MzXG3r\n7LOEZbB0f757fZSQAFOPXtv1TW0cOF5Be4eD8xUNzhEIg9bVyUSv03qlxe7Ne3Xoh8cWTeKBufFE\nDbIO0hMCfY2sXT6NuAj/W6rlmazcNTWSw19WUXDmUo8ndXf85YuLFJXWkRAVyJnyej4/e5lxQT78\n2+o5/R7Lyw2tCJxZCvDeTWI0aWhq4x8XT+6RIZxxWxh3TLFy8EQlLa3Oi+utmNm+nqV3TeSr8gYy\nksN5YG48YWEBWIOula89dHcChSW1tHfaMei1pE4I7bG/zCY938tOYVuAiY+OlXPxchNzUqz8bvcZ\nHELw8tsFZCSHc7SohkBfQ59tMYcbGTPZQ2FCZCAvPjGbTz6/yAeffs1/bjuO2aQjdUIoUxNCEcI5\n0b2otI6m61apffDOeB6an+BF5SNPbEQAH//twqi147OPchnJYBmJrlHR4f6YTXp+/eeTRIb6UmVr\nwV2jzR8+nEbKAN3MznVNzJ/gwSiuQa9zPUQsuSOe17cXsudv5QT5Gfnth6eJDvPjnx+Zgdmkx+5w\ncKGmmV//+SS5v/8cgOdWTMPf3DNzfXt8CCaDjk8Lq5kQFXjDrRH/Hlew3bV4liXA5Cojaeuw84tt\nxymraUKv0xDga2TlwiTuGaYRiKFwSwbbZpOe6FGYUT2ck5QUQ+O28cGEB5v564mKfoPt9g47f9pf\n7JxVfboGH6OOuSlWjhRWcfjLKu6e1vcyvJcbujuRjE6gIwNajcbteT5vSiT7Cy5y7HQ189OinX22\n9XLdNEcTf7OBF1fN7vPfDXotaUnj+v0OrUZDTlYS48P9+d3uM5wuq2diVCDffTCF3+46zaGTVcxJ\njmB5ZuKodN65WTEadCyaHcs906MpKq3j87OXOFFsc/VdDvIzMmViKCkTLC6vd0/UupmJDfen0+6g\nqralV8eWE8U2/Mz6AecU3AjdnXxuhRGxQF8jLz2ZwaeFVZw8b2PmpHDuSLWi1UB9Uzut7Xbe+vA0\n/3ekdOBg+2ID48P98RniSEv6pHAiQ0v4475zgDP7/oMVaa45DjqtljhrAM8/NpPNOwpJigl2u4aI\nj0nPi6tm42PUETDEyZFwrWa7O7NtCTBRXtOEEII3PzhFeU0Tzy6fJl38NaijUVpayrp166ivryc4\nOJhXXnmF2Nie9S4Oh4MNGzZw8OBBtFotTz75JMuXLx8R0QrFjaLRaLg7LYp3PimmpLKxz5vj387U\n0NLWyY9XTicixBeTQYfZpKPS1szOw6XckWrtM6vT3bpptLKKfTGafo2PDHA7mSzeGkBkqC+Hvqxi\nelIYQtwaN83R4M4pkcRFBHCkqIoH5sTj66Pnhw+nUdvYOqz9tW91jAYdaUnjSEsah0MIyqub0Go1\nxIT5DfuI6Fi4x47vniRZ3eQKtjs6HWzde5ZPPneWSN0eZ2HRrPGkTAjpdZ2su9LG1r1nqbI109LW\nSUyYP9MSQomPDCTIz8i+4xXszS/DbNITYTEzKdbZQvdWGCEEZ9C4eE4ci+fE9djeXTqyaNZ4/rjv\nHOcrGvuce2R3ODhf2cidA4zeDgatVsMPVkzjQk0zAb4GYsL83Wb1g/xN/PiRGf1+13DeE/2uq9kG\nCAn0obG5nf/44xcUldbxrXsSpAu0YZDB9gsvvMCjjz7KkiVL2LFjBz/96U956623erxnx44dlJeX\ns2fPHmpra1m2bBl33nknUVF9ZwIVitEkc3o0Hxz5mp2HS1nzzalu33PgeCXhFrOz5v66G2r2vAn8\n8p0THDpZyfy0aLefvVR/FYNeS5D/0J/eh8Jo+vX2OPdZFo1Gw7wpkfzpk2LWv5mPXqd19Z9XDJ2Y\ncH+Whye6Xmu1GhVojyBajYY4a8CIff9YuMdaQ5xzUT7+7AJ/OV5B3ZVWWlo7aW7t5L7ZsQT6Gfkw\nv4xfvnOCAF8DlgATHZ0OYiMCmBQbzPaDJbS22UmOt2Ay6ii+2MCJYluP35jcdd09UWzjSGH3ROJb\nI9geiLunRZF3qJRdn37N0w9NcW13OARtHXY6Oh18XXWFtna7R/Xa7hgXZJZupNZVRtIVbIcG+iCA\nsuomVmYlsTC992RoGRgw2K6treXUqVM88MADACxZsoQNGzZQV1eHxXLt5rlr1y5WrFgBQEhICAsX\nLuTDDz/kiSeeGCHpCsWNYTbpWTRrPO8fLKGs+oqrnVU3lbZmviqv51v3JPTKXE1NCCUxOog/7D1H\ndJi/24vZ5fpWxgX5eLWOdbT9mhzfdwA9J8XKewfOo9Nq+JdHZ9wSQ+0KxY0yVu6xOq2WxOggTpfV\nEW8NICE6CKO+K/uf6CyBWpgew8nzNo6dquFqWyc6nZYvz9s4WuRsSPDDFWnEdPXsFkJQU3+VCzXN\nXG64yl0zxuPbVWp2ta2TvMOlHD5Z2WtJ8VsVs0nPgpnR7Dz8NWt+cQCA9k6HayLp9cjWgnM4SYoJ\nZuakMNf9ZPbt4Rj0WqYmhI7agkueMKCyyspKIiIiXMGHVqslPDycqqqqHheCioqKHk/YkZGRVFZW\njoBkhcJzFqbHsPtYGW98cIqk6GCMJj21DVdpa7dTU38VnVbjdghOo9Hw9LJUXv7fAn6x7TjLMxMw\nGXQY9FqMXbOcL1xuJsLi3SzAaPs1LNiMw+FuKo8z8/DCP83CEmhSfYsVij4YS/fYtd+ait0h+gxq\n9Dot05PCmJ50bRJcp91BadUVokL9enSi0Gg0RFh8XR13ujt+gDOwXJGZyIrMRBTXuG92LHaHoL3d\ngUBg1OsIDjLT0d6BUa/Dx6hjXJCPdNno4cQSYOLpZdcy+0aDzqMFw0YbrzwGNDY20tjY2GObTqcj\nMjLSKy1ZBovS5jmy6PP3NfLIP0xif8EFiisa0Oq0mPTOtkDRYX4smBmNJdB92zRLoA//8ugMXn+/\nkF1Hy9y+Z1KsZdj+r93fU1lZid3ecwndwMBAAgNHJ1M8FL/GjuDQ+0DIcs71hcz6lLYb52bw60D4\neJA5NGp1g14IR9ZjC3Jo8/c18vCCpB7bQkP9sdlGryWjJ8iw7/6e0fbrgM6JjIykuroaIQQajQaH\nw0FNTQ1Wa8/sX1RUFBUVFaSmOvuvVlZWEh3tvrb1rbfe4tVXX+2xbcaMGWzduhWLRd4V90JD/Qd+\nk5eQWRvIpW9pZhJLM5MGfqMbQkP9+fmz84dZUf8899xzFBQU9Nj2/e9/nzVr1vR6r/LrNWQ659wh\nsz6lzXNuxK8w/J4dq34FuY+t0uY5Muu7Ub96jBgEjz32mNi+fbsQQoj3339fPP74473e895774lV\nq1YJh8MhbDabmD9/vigvL3f7fQ0NDaK8vLzHn2PHjomcnBxRUVExGEmjSkVFhcjMzFTaPEBmfTJr\nE8KpLycnRxw7dqyXXxoaGvr8nPKr/MdVVn1Km+d46lchhtezY82vQsh9bJU2z5FZ31D86gmDGhNa\nv34969at47XXXiMoKIhXXnkFgNWrV7N27VpSUlLIzs7m+PHjLFq0yFnf+vTTxMS4nxXaV4q+oKCg\nVzpfBux2OxcvXlTaPEBmfTJrA6e+goICrFZrn15yh/Kr/MdVVn1Km+d46lcYXs+ONb+C3MdWafMc\nmfUNxa+eMKhge+LEiWzbtq3X9i1btrj+rtVqWb9+/bAJUygUnqH8qlCMLZRnFYqbG9XAUqFQKBQK\nhUKhGCFUsK1QKBQKhUKhUIwQuvUSjUuZTCYyMjIwmUzeltILpc1zZNYnszaQW5/S5jky61PaPEdm\nfTJrA7n1KW2eI7O+0dSmEUK4X5FCoVAoFAqFQqFQDAlVRqJQKBQKhUKhUIwQKthWKBQKhUKhUChG\nCCmC7dLSUnJycrjvvvvIycmhrMz9UtijQX19PatXr2bx4sVkZ2fzzDPPUFdXJ53OV199lcmTJ3Pu\n3DlptLW3t7N+/XruvfdeHnzwQX72s59Jow1g//79LFu2jKVLl5Kdnc2ePXu8pi83N5esrKwex3Ag\nLbLsR1l0gPLrUJHZszL5FcauZ2XQ0M1Y8SvI6VmZ/QpyeVY6vw77Mjke8Pjjj4u8vDwhhBDbt293\nu3rWaFFfXy/y8/Ndr3Nzc8Xzzz8vhJBHZ2FhoXjyySdFZmamOHv2rDTaNmzYIF5++WXXa5vNJo02\nIYSYNWuWOHfunBBCiNOnT4vp06d7Td9nn30mqqqqxIIFC1zHcCAtsuxHWXQIofw6VGT2rEx+FWLs\nelYGDd2MBb8KIa9nZfarEHJ5Vja/ej3YttlsYtasWcLhcAghhLDb7SI9PV3U1tZ6WZmT3bt3i+98\n5zvS6GxraxMPP/ywuHDhgutCIIO25uZmkZ6eLlpaWnpsl0FbNxkZGaKgoEAIIUR+fr649957hc1m\nE+np6V7Td/3FvL99Jct+lEVHXyi/Dh7ZPSujX4UYW56VQUN/yOZXIeT1rOx+FUJOz8ri10GtIDmS\nVFZWEhERgUajAZyrZIWHh1NVVYXFYvGqNiEEW7duZeHChdLo/NWvfkV2djbR0dGubTJoKysrIzg4\nmE2bNnH06FH8/PxYu3YtPj4+XtfWzcaNG3nqqafw9fWlubmZLVu2UFlZidVqlUJff8fR4XBIsR9l\nONf6Qvn1xpDds7L7FeT3rCznmjtk9CvI61nZ/Qrye9abfpWiZltWXnzxRfz8/Pj2t7/tbSkAfPHF\nF5w8eZKVK1d6W0ov7HY75eXlpKam8u677/KjH/2INWvW0NLSgpCgu6TdbmfLli28/vrr7Nu3j9/8\n5jc8++yztLS0eFuaYphQfr0xZPas8uvNj2x+Bbk9K7Nfu/Upz/aN1zPbkZGRVFdXI4RAo9HgcDio\nqanBarV6VVdubi5lZWVs3rxZGp35+fmUlJSQlZWFEILq6mpWrVrFunXrvK4tKioKvV7P/fffD8DU\nqVMJCQnBZDJRU1Pj9eN76tQpLl26RFpaGgAzZszAbDZjMpm8vu+66e8c6z7e3tYpgw/cofx648js\n2bHgV5DfszL4wB0y+hXk9qzMfoWx4Vlv+tXrme2QkBAmT55MXl4eAHl5eSQnJ3t1iGvjxo0UFRXx\n2muvodfrpdG5evVqDhw4wN69e9m3bx8RERG88cYbLF682OvaLBYLGRkZHDp0CICSkhJsNhsTJ070\nujYAq9VKVVUVJSUlABQXF2Oz2YiPj/e6vu6sRH/nmAzn30AavYXyq2fI7FmZ/Qpjx7MyaPh7ZPUr\nyO1Zmf0KcntWBr9KsYLk+fPnWbduHY2NjQQFBZGbm0t8fLxXtJw7d45vfOMbxMfHu5bwHD9+PJs2\nbZJKJ0BWVhabN28mMTFRCm3l5eX85Cc/ob6+HoPBwHPPPce8efOk0Aawc+dONm/ejE6nA+CZZ55h\nwYIFXtH30ksvsWfPHmw2G8HBwVgsFvLy8vrVIst+lEUHKL8OFZk9K5NfYex6VgYN3Ywlv4J8npXZ\nryCXZ2XzqxTBtkKhUCgUCoVCcTPi9TIShUKhUCgUCoXiZkUF2wqFQqFQKBQKxQihgm2FQqFQKBQK\nhWKEUMG2QqFQKBQKhUIxQqhgW6FQKBQKhUKhGCFUsK1QKBQKhUKhUIwQKthWKBQKhUKhUChGCBVs\nKxQKhUKhUCgUI8T/A5y9YImR4UyVAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x271692e2b8d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "f = plt.figure(figsize=(12, 4))\n",
        "for i, param in enumerate(sts_model.parameters):\n",
        "  ax = f.add_subplot(1, len(sts_model.parameters), i + 1)\n",
        "  ax.plot(samples[i])\n",
        "  ax.set_title(\"{} samples\".format(param.name))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tZOydxU53oE9"
      },
      "source": [
        "Now for the payoff: let's see the posterior over Poisson rates! We'll also plot the 80% predictive interval over observed counts, and can check that this interval appears to contain about 80% of the counts we actually observed."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "56rIH8MCeU9F"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x27169aafdb90>"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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NqqpKfD4vLlc6pqayKwRBEIR2aWwXdF1vrHC7jiRJKIqCpv14UjjccEnO4f9e\ny7JMLBZt9L42m52XXnqd9evX8t133/C3vy3muedexulMbetH6VRiBXgHMypGkkxJpKgOkkxJ+CNe\ndrl3sqFsHdsrt1ARKCMY7ZiitR3t2WedPPuss13XOPHEMGPGBAiHj/+RKVmWsVptaJpGUdFBamrc\naNqxA1FBEAShdUaOPIl9+/awZctmIP5Dc2pqKpFIhPXr1wKwbt13xGIx+vXLJSenD0VFhXi9XnRd\nZ+XKf7foPjabrcEUqNvtJhgMMn78qVx33U3Y7UkUFhZ2/AfsIN1viOM453F7WPXRftyVRhyuCJPP\nycXhcNSvhdtXsxcdHbPBQpo5nRRzSreoC1dZqVBSYmDixPZl+uTlRfj1r90d1KruwWg0YTAYcLvd\n9aNuqtp71y4KgiB0tOTkZB544GEWL36UQCCAosjceOOtLFjwEI899nB9IsKCBQ9hMBhIS0vn0ksv\n59e/vpycnD4MGzaCffv2HPM+gwadSG5uf6688lJyc/P4xS9+xaJFD6BpMWKxGKedNpGRI0cl4BO3\njaTrjQ1KHn+Wf7WiwVBpV/C4PTz/11I8NRciySq6FiI5ZSm/mpNJsiO5wXsjsTCBWABN1zBIRtKs\naThUBzajHbkL1sF99pmV119P4Z57ysjIOHa5D6fTSnV190rlToRIJEI0GiY52UFKiiOh5UrS05Mo\nL69N2P0E0eddQfR5YhzZz72lTltXOLKvZVnC5bK36Vo9ZqQtEPWjypYubcOqj/bjqbkMSY6Pwkiy\niqfmQlZ99AozZo9s8N7DM1JjWpQKfzklvhJkScapppJqcWE32jDIicle3LJFJT092qKArTczGo0Y\nDAZqa2vw+/24XC7M5q793gmCILRXbw+sjhc9Jmh7cc8LBMNBsq05ZFuyybbm0M+WizFBQQ+Au9JY\nH7DVkWQVd1XzbVBkQ31hX03X8IRrqAxW1NeES7Okk6KmdFoAFw7Djh0qp5/e+0bO2kKSJMxmK9Fo\nlNLSEpKSkkhJcaIovStTWBAEQUisHhO0GWUDZZEaPDU1/FCzDYDrhtyIy5yWsDY4XBG+36BhtSkY\nDPGpWl0L4UhteTkLWZKxGeO5qLquE4qF2F2zCxmJVHMa6dY07KYkpA7MIQkEZEaPDjJ6dPdMkOiu\nDAYDiqLg9XoPjbqlY7GIUTdBEAShc/SYoO1Xg35DRaCCYn8xxYEiyoPlpKquo96n6zrP7/oHDpOT\nHGsOWZYpFZMuAAAgAElEQVRssizZqB1QFHf46MG8v/TfBAPnkpGlE42GsZjfZvI5uW26niRJmA1m\nzAbzoRE4N5XBCoyykUxrFk5zKmaDud3tTknRuOqqjk0e+PxzK1arxpgxPTsQjI+6WYjFopSWFmO3\nJ+F0OrtdsWBBEATh+NdjnixffLCXkyakMSr1JEZxUpPvqwm7KfIXUuQvZKs7nlosIZFhzuQ3g69p\ncxFVXYevPh1F7sAAQ4Y/h9drYO+OFKz200lKKWrTNQ8XH4GLL1yMalEKvQc4ULufFDWFTGsWSWpy\ntyrku3q1FZMpMUFbdXU177yziYoKibQ0nfPOOwmns32lS1pLUQxYLAqBgI9AwE9qahpWq1UU5RUE\nQRA6TI8J2rZuPp91377Jr+ZwVKbm4ZJMyfxm8LWU+Iso8hdREiimLFiKLMmNPmDDsTBV4SoyzZnN\nPoB/2OykYHcS/z2zmnETRwCw4ds03nsjh/17PfQf2HFbYxhkAymqA4BANMBO9w5kSSbDmoHLkobV\nYDvGFTpfbm6Yb7+1oGnQmQmW1dXVPPTQRtzuC5FllZ07Q2zbtpQ77xyd8MBNkiRUNb7DQ3l5KTab\nDafT1S2LBwuC0LvFYhrp6Uld3YxeIRbruPqePeZpImFqMlPzcIqkkGXJIsuSxcmufCA+cuWP+hp9\nf4FvH6/vfQWzbKafPZdcW39y7f3JtGTVj2xFIhIr3+tHelaA/FPL6s8dMbqKj9/ry9rVGR0atB3O\nYrBgMViIaVHK/eWU+IqxGCxk2bJxqM6EZZ8eKS8vwuef2ygtNZCd3Xgl6o7wzjubcLsvJBIxU1Zm\nICcH3O4LeeedZfzyl2d02n2boygKVquNUChIUdFBkpI65h9GWQ4TiUhiP1RBENqtqurHZ54os3L8\n6DFBW021GUnmmJmajTHIBpJNKY2+FomFSTE6qIm42enZwU7PDgBOcp7MebmzANi/JwmP28TPf/sD\nhycQGk0ao8dW8u2XGdR6jCQld97+mopsIOlQBmooFmJvzV4k9uI0u8iwpnd48sKx9O8f/6wFBcZO\nDdoqKiRkWaWkxIDHI6Mo8cCtsrLrpyVNJjOaFsPna/wHgtZSlBhut4/U1DRsNruYehUEQehlelTQ\npkm+VmVqtsRw50iGO0fiDrs54N1PgW8f+70F9LH1rX/PoCEebvjDJhzOMIX+QqJahBxrH4yykfxT\ny/jm80w2rEln0tntX9vWEqqioioqmq5RG/ZQFaw8LHnBidkQz3D0+yVeesnB1Kle8vI6tt8yM6Oo\nqk5BgZFTTw106LUPl5ams3NniLQ0mdpamaoqhdRUPy5X96gZLcsKJlPHrDW0WCz4/TEqKsrx+32k\nprowGMSomyAIQm/R4qAtEomwceNGysrKmD59On5/vKaX1Wpt8c1uvPFGCgsLkSQJm83GvHnzGDp0\nKPv27eOuu+7C7XbjcDh46KGHyM1tXcalwRigqvIDxp8+oFXntZTD5MCR6mBUajzJ4ciNJBzO+Ga1\nX5d9yfaabSiSQh9rX/LsAzhpWhV5AxO/+ezh5UPqkhcOevdjN9rJsGaxe2smmzaZOfvsjp+6lWW4\n+OIaMjI6b5QN4LzzTmLbtqXAhQwdqrFjh05t7XJmzGg6GeV4VrcfanzqtRCXKw2r1SZG3QRBEHqB\nFgVtP/zwA9dffz0mk4nS0lKmT5/Ot99+y7Jly3jsscdafLNFixZht8czID/++GP+9Kc/sXTpUu65\n5x6uuOIKZsyYwfLly7n77rt54YUXWvVBJkx6he++OYNVH8lc9IvddPYzrKmHZJo5nYxQFWXBUvb7\nCtjvKwDnp4x0/gIY2LmNasbhyQuhWJA9Nbv56GsjmtGEM7uMqJaEQe7YgdfOHGGr43Q6ufPO0bzz\nzjIqKyVycgy43WcgSRrQczd3V9X41Gt5eRk2m53U1FRRZkQQBKGHa9G/8vPnz+fmm2/m/PPPZ9y4\ncQCMGzeOefPmtepmdQEbQG1tLbIsU1VVxbZt2zj33HMBmDFjBvfffz/V1dWtyv6bPrs/znQ/X32a\nTY3bVD/ylWhnZJ3JGVlnEoj6KfAWUODdxwHffvra+jX6/k1VG8mwZB4zO7UjqYoZk2ymcHcmfQdV\nstuzA8kDTrOLdGs69i7a/7StnE5nfdJBLAahUAyrtXtMj3YmWY4nPASDgQajboIgCELP1KKgbdeu\nXcyaFV90XxdYWK1WQqHWby47b948vvzySwCeffZZiouLycz8MWCRZZmMjAxKSkqOCto8Hg8ej6fB\nMUVRyM7OBmD8pFJG5ldis3fulBxAwK9gsTa9T6fFYGWoYxhDHcOavkY0wLsH3kZHx6xYyLX1J8+e\nR3/7ANLN6Z0axBUdsOH3GRk+wodDdTRY/6ZIMi5LOi6LC5vRltAEhvZSFHpFwHY4VTUTi8UoKysl\nKSkZh0NsqSUIgtDdFRcXE4s1jCOSk5NJTm66bFmLgrY+ffqwefNmRo0aVX9s06ZNrV53BrBgwQIA\nli9fzqJFi7jllluOWh/WlBdeeIG//vWvR7Xtk08+wWZVQYL4Z+3caaKAX+HZx4Zy+pRyJp9TduwT\nmqCFQozLHsuemj24Q272+Hayx7eTFHcKd5xyR+cGbfvTMBplRo8JYbXFd1VIIb4+UdM1/BEfB0Ju\njFEjWbYsXFYXFoOlQZuczpavZ+wMHo9ELAZOZ+8J0prrc123EwwGCQSqycrKEltqdRBRyyrxRJ8n\nnujzxLv88sspLCxscGzOnDncdNNNTZ7Toujmlltu4dprr+XSSy8lEonw1FNP8eqrr3L//fe3ubEz\nZ87k7rvvJjs7m9LSUnRdR5IkNE2jrKyMrKyso8658sorueCCCxocqxtR8PlDaFpiHt4fLu9HrUci\nJ7ec2trWVfx3V5mw2qKYVA0ZlXMypkMGuEPV7PPuo8C7F5vRjtd79ChmTbiGQv9BBtgHYDG0L2A6\n5dT95ORWENN81DZanseAAQPRUJQdnj3E9J2YDWbSLZk4VCfZ6alUV3ftBvNLlyaxapWNhQtLe8Xo\nmtNpbVGfR6MhKip2kJLiICXFgdyZ1Y17OFG/KvFEnyee6PPEkmUJl8vOyy+/3OhIW3NaFLSdeeaZ\nPPPMMyxZsoRx48ZRWFjI4sWLGTmy6SK2R/L7/Xg8nvpg7JNPPsHhcJCamsqwYcN45513mDlzJu+8\n8w7Dhw9vdD3bsYYNE6GsxMJ3qzPIn1BGZk7rFtpXlqs89cgops4qYMxp5Q1ec6hOTladnOw6pcnz\nf6jZzkdFHyAhkWXJJi9pIAPtA+lr69fqJAKDQadP7rHrh8Xrv8X7PBILc7D2APtrCyiLuVCjSSSp\nSfERuCamUL//XuX995O4+eZKzOaOC6wiEfj6aysjRwabDdhiMfB4ZJzOnpuUcKS6jexra2sIBOIb\n2atq+/fWFQRBEDpO3dKu1mjRk76oqIihQ4cyf/78BsdLSkoaHRFrTCAQ4JZbbiEQCCDLMg6Hg7//\n/e9APNHhrrvu4sknnyQlJYVFixa17lM0QdPg68+yGH5yVYckJug6fLg8F1WNccbUwmOfcITUtBBZ\nOb540HdqeaszXJONyfS3D+Cgbz/FgSKKA0WsLvuC0zMnc0bWma1uT2sZFRMpiqn+zwdqC9BrQUbG\nYXaSak7FarShKj8GCJIUL7B74ICRE0/suOSQtWst+Hwykyc3P/L097+n4vHI/OEPFZ26nVZ3E9/I\n3kokEqG4uBCnM5WkpGQx6iYIgnAca1HQNmXKFMaNG8fixYtxOBz1x6dPn866detadCOXy8Vrr73W\n6GsDBw7k9ddfb9F1WsPrMfLVp9ns2OrgF9dtp71rs3/Y4qBgdxJTZ+1vNgmhKZIEY/6rjHeXDGD/\nXnurt7aqS2yIaBH2ewvY693D3to95Nkbr01X7C/CbkwiydjxaxVMiqm+hEhMj+E9lMQAOqpiJtWc\nSrKaQp9+8XsXFHRs0LZqlY2srOgxrzlhgp/nnnOyerWViRO7djq3KxiNRgwGBbe7Gr/fR1paOkaj\n6dgnCoIgCN1Oi37stlgs5Ofnc9FFF7F9+/b64y1NIEgEf8SPL+wlGA0SiYWJ6TGSHRGmXVBA4X47\nn3/Up933yBtUy5k/PcgpE9qefDD8pGrMlihrV2e0+RpG2cig5BM4O+e/uXrIdfS35zX6vncPLOcv\nWx/lqe1/46PCf7PLs5NQrHVr8FpCkRSsRhsO1RHf71QyUO4vY0fVdnYHvkWxVbBlZwh/1IfeAbXT\nCgqMFBQYmTzZd8zRyjFjgpxwQpjly5Pw+3tnAVpJkrFYrGiaRlFRIR5PTbf6f1cQBEFomRYFbZIk\ncdttt/G73/2Oq666ig8++KD+eHfRN7kfLmsaFqMFDR1/xE9NyE2fYXsYcsoBPvskjc3bwBPy4I/4\nCMWCxLRoqx5eZkuM/zqzpF0jdkaTxuhxFfyw2Umtp/O2IIppMZKNKRhlExWhMtZUfM1re/+PRRse\nprym4wO3wxkVI3ZTEimqg2RTCpl9PWzfHWVLxWbWlaxlt3sX1cEqQrHWl4wBsNk0zjjDx/jxx15T\nKEnws5/V4PPJrFjRu7OjjEYTqmqmurqSsrJSotHO2wtXEARB6HitWr0+ffp08vLymDNnDtu3b+9W\nP62nqmk4Ta4GxzQ9RkSLcsIvYzxSovLF2+O5/vYdGFQfwViQcCxMOBafotQB6dB/ZSQU2YDh0C+l\ngwvN5k8oB11Ckjqv/xRZ4ZKBlxHTYhz0H2Bv7R72efeyc4/EP5f9F7ffsx6j8cf7x/QYm6u/p5+t\nH05TaocF5JIk0S83zM7NGRgjaZhtoUanUpNMKVgMZkzKsRfMp6XFuPhizzHfV6dfvygTJ/r57DMr\nkyf7yMho/dR2TyHLMhaLjVAodKggbzo2myjIKwiCcDxoUdB2eKHO4cOH88Ybb3DTTTcRDHbuiE17\nyZKCqiioNrj2tz7efjuZdHM2KSmHT9HpRLVo/JceJRqLEowFCcaCBCJ+ApEAMb1hsV4JGaNiQJHi\nQZ0stW5xd2paiLNnHOiAT3hsiqzQ355XP4X69+XDSM7zNgjYAMoCpbx74G0AbAY7/Wz96GfrT669\nP1mWliWbNOWkMRUMO6kKqy2KdGgqta5gSSQWodxfRrGvGAkwKSopqoMU1YHFYGmQ1NAe553n4YQT\nQqSn996A7XCqqhKLxSgvLyUUSsbhSBVJCoIgCN2cpLdxuCwWi1FSUkKfPu1fK9YRtm7d3WkjfzE9\nRiQWIaqFiWhRgtEggWiAYDRAIBZA1xuu05IlBYNswCQbUTp4P8/2cFeZeGLRSZw94wATJpU2eK0k\nUMKXpavY79uPP/pjKZA8+0AuH/SLo66VlGRudY26lohqUULRIBE9CugYFRWH6iDFlILFYMVsUImP\nifY+La3T1hq6rhMKBTEYDKSlpWMyidIghxP1qxJP9HniiT5PrLo6bW3RZETx7bff1u8zunr16iYv\n0F2Cts6gafDiiw4mTfIxaJACmBt9X1SLEtHCRLVIfVDnj/rwRnxEIrVISEjIqAYVk2zqkrWAHreH\n156rpLy4lIJdJQwb1Ydkx48177IsWVyUdzG6rlMVquSA7wAHfPvJseY0er0DtQfYXraToSnDcKgt\n3yP2WAyyAYPpxy9zTIviDlZT7o8nfxik+Mb3DnN8JM5isNBbg7iOEC8NYjlUGqSovjRId1qvKgiC\nIMQ1GbTde++9vPvuuwDMnTu30fdIksTHH3/cOS3rBr76ysq331o46aQg0PSi7bq1b40Jx0IEY0G8\nYS81ITeecE39a0bZiKqonT4a53F7eP6vpfyw5ReEI1Z2bC2npHApv5pDg8AN4n+nLnMaLnNas4V+\n15WvY3Xx13xc/BGZ5iyGOYYzJGUYaea0Dm27IhuwHeofj9uIJTlAbbiGqmBFfP2hJJOipuBQndiM\n1kM7RYiAo7WMRiOKolBdXUUwGCQ11YXB0H1GiQVBEIR2TI92N22ZHtV1miwZ4fdLzJ+fQXZ2lFtv\nrWx1IdymaHqMYCx4KLu1Bk+oBrdbwp4SQZEUVEXFKBs7dKTj3SWb2bDmMirKHSiKTmpaEF0LcfL4\nV5gxu+W7WhyuKFrAN4XfsdOzg4j2Y62083MvYoSzbddsTlWFyt//PIrpF+3j5HEV9cdjeoxwLEQ4\nFkZHxyibyLRm4TQ7MRt61t6bnTE92phwOIiuQ1paRq/fv1RMGyWe6PPEE32eWJ0yPdqUPXv2sHv3\nboYPH35cT436/RL/+IeTU0/1M27c0Wuz3nsvCb9fZvbsmg4L2CC+3s1qsGE12EizpPPee3Y+XGlh\n7vzdRBQPNcH4aFxdNqtJMWFS1HZlsLorjUiySnrmjyUyJFnFXdX2kiNDnEPIMfQnokXYW7uH7TXb\n2O3ZSV5S44V+IT7dHI3ImNTW12pb9006SDqDhtQ0OK5IChaDtX4v1qgWpch3kIPe/dgMdjJtWaSo\nKRjkhp/100+tFBcbueyyhtcTwGQyE4tFKS0tFvuXCoIgdCPNBm3/8z//w7Bhw5g1axYAb731Fn/6\n059ITk7G7/ezePFizjjjjIQ0tKOpqk44LPHqqynk5UUaZBUWFRlYtcrK6af76Ns32sxV2m/48BAr\nViSxfWMWkycn08fel5geiyc5RAO4Q9V4Qh5ierx9BknB1MrROIcrwr7dIST5x0XmuhbCkdr+Ol1G\n2cjglCEMThmCpmuNZtLGtBj/3PksOz+dxLh+J/Czaa0bSYxEJDZ9l8aQEW6Skptvs0E2kGxKASAU\nC7K3ZjcADrOTdEsmSSY7sqRQWyvzxRdWxo/3M2iQqFd2JEUxYLHU7V8aID1d7KQgCILQ1Zr98Xnl\nypX1yQgAjz76KHPnzuXrr7/m3nvv5Yknnuj0BnYWRYFf/cqNJMFzzzmJHhabeTwymZlRzjuv84eL\n8/Ii9OsX4bPPbNTN7iqSgs1oJ82SzgmOweRnjmFU2mhOdA4h3ZYZb2O4hpqQm5qQm0DUT0xrOric\nfE4uySlL0bV4MVtdC5GcspTJ5+R26GdpqvTJfl8BZcESPJkf8El0MX/Z+r98cHAFBd59Lbru1o2p\nBPwGxp7Wup0oVMVcX+DXF/byQ/U2NpSt42DtfiaeWYrTGeP111PQes9e8q1St3+prmsUFxfi9dZ2\nq9qMgiAIvU2zQVtVVRU5OfHswR07duB2u5k9ezYAM2fOZN++fZ3ewM7kcsW4/PIaCgqMvPvuj9Xy\nhw4NM3duBTZb5z+gJAkmT/ZRUmJg166mRjIkzAYzDtVBX3s/RqSN4pTMsQxzjSAvZSBWo51ANIg7\n5MYdcuMN1xIIRSgriY+sJTuS+dWcTE4e/wr9B77MyeNf4VdzMo9KQugsefYB/PKEXzPUOJmYJ5Pa\nSC1rK7/l67KvWnT+2tUZpGUEyR3YtiBakiSsRhtO1YnVYKXMX8Yu7/eM+sk6dhdofPq5WHDfHKPR\nhMlkprKynIqKcmIxUetOEAShKzT7tEpKSqKiooK0tDS+++47Ro4cickUDyyi0dZtAdVdnXJKkEmT\nfKxYEWLfvs/RNJ20NJ3zzjsJp7PjSlk0Z+zYAMuWJbNqlbXFm6rXjcbVjciBTigWJhANUBPw8tJz\nGezZZePK277BZo9gspuYdtHQLqkbJ0kS/Wz9mJJ5Mt5V13Lh5A8pNW4gx9r4msgD3v14Ih7y7HmY\npSQGDakhNS3UIWsLFdlAkikeoNtGV7N2dTH/96YV58Dt9E9PJ9mU0mQmcGtVV1fzzjubqKiQEv6d\n6mh1OykEg36Ki4OkpaVjNvfuJAVBEIREa/bpNG3aNG677TbOOeccnnvuOa6++ur61zZu3Ei/fv06\nvYGJMGVKAStXbmb79lkoisrOnSG2bVvKnXeOTshD1mSC//5vbzuDEglVUTGg8uabeRTvsnDF7GrG\n9h98aG2cm9qQh6gerS+IYVJMmGRTwgK5nH4+JCSiZYM5c6yryfetq/yOze7vAUhTMxgwYgAmex7B\nWB5mpfFaeW1hMpg478JSVr6biz8Iu927kIBUcxrp1jTspiSklm3Pe5Tq6moeemgjbveFyHLiv1Od\nRVUtRKNRSkqKcTicJCeniCQFQRCEBFHmz58/v6kXJ0yYQElJCWvXruWss87iqquuql9AvnLlSk4+\n+WRGjuz48g5tUV5e3eZz33xzDUVF56Mc2jJJkgwEAoPx+z9j9Oi8Dmph8wYNijBwYPsWxGsavPSS\ng7VrLVxwgYezpgQwKSasRhupZhfZ9mzSLek4zA5sRjsaOv5YgEAkvhdrKBYkpseQkFDk5rNVVdVA\nONy6JA2zNcqGNelk5fjp29/X5Pv8MT8xLYY34sUbraXIX8hW9xb6Wvvh6uA6cPakKCeNqcRmjU9B\nmxQTvkgtpf5Syn1l6OgYZANGuXWZtkuWrGHXrnjABh3znbJYjASDXZ80IcsyBoMRn89LMBhEliUi\nkXC7f0WjESRJQj7Gdy+RbDYVv79lo99CxxB9nniizxNLkiSs1rYldjU7xGI0GpkzZ06jr1155ZVt\numF3VFEh1T9c68iySmXl8VWk9dVXU/j2WwvnnVfL2Wc3FhRJmBQVk6KSZEohwxpPaohqkXjQFg1R\nG6mlNuzBH4qfrxPPWDUeGpVrT/04WYab52485ohivmsM+a4x8fId/kIKvPvY591Lrr1/o+9fX7mW\nVNVFH2vfdk9typIcn3YmvhtDia+IQu8BrAZbffkQo9zwfzZdhwMHjHz3nRlFgVmzaht8p3QdCgqM\nJCUpVFQcX9+ppkiShMViJRIJU1FR3mHX1XUds9mM3Z6E2WwRBX4FQRAOI/5FBNLSdHbuDDUI3DQt\nhMt1fK3ZGzw4hMMR46c/9bbqPINsxC4bsRuTcFniI1nxorVBgtEQ3kgt3rAXT9iDjgZI6CYrmia3\nemq1NTGfQTaQa49vWj+JxkvLhGNhPjj4PhoxDJKRgUmDGJIyhBOTB9fXbmur+Pq3eLJGKBZib80e\nJH4sH1Jb4WDdWjvr1pkpLzegKDr5+fGaf4d/p+qyU4uKouzaZaa6Wsbp7Bkpq0ajqcNLgUSjUaqq\nKtB1UFUzSUlJmM1mFEX8cyUIQu/Wq3dEqHPk+iNNC+FwHP/rjzqajkYoGiIUC6NYouws3kdUj2Ix\nmFE7cK0ZQDCgoJpjxwzyfFEfX5V+wT7vXsqCpfXHrQYbtw7/XYfvoanrOoGon1qfxjP/czoGSWXE\nMI1Tx0UZPTpYn3Hc2HcqFnsbVZ2CqqZy8cUexo0LtCqITdSOCN2FrutEo1Gi0SigY7FYsdvtqKoZ\nRUnMFKqoFJ94os8TT/R5YrVnRwQRtB1Sl+lXWSnhcnVtpp+uQygkYTZ3378ap9NKZVUtnpCHYl8h\n3ogXg2TAarQ1Wa+tNV7954lomsTPf7ujxed4Ih521vzADzXbSTalMKPfzKPeo+kaElKTwVzh/gAr\nlxeiGGI4XJF4jbsmSqP8sMVOclY5FnsQi8FCpjWLFNWB6dDayMa+U9FoGi++6GDPHhPXXFPF6NGh\nFn++3ha0He7HAC4CSFitFuz2JFTV3KmJEOJhlniizxNP9HliiaCN9gdt3UUsBgsXpjN4cIhLLvF0\ndXOadGQA4Y/6KPOXUeGPF8C1GmwYlbZtk1W3z+jpZxUx+ZyiNl1D1/VGA7P1lWtZXfYVg1OGMCR5\nKH1sfeuDTI/bw8K7aikrvoQ+/SME/DF07R2uuC6bU8Y3f79wLEwg6kdHP2z3haRGtx/TNPjuOwtj\nxwZoTbzRm4O2w8UDuMihxAUZq9WGzWZHVdUOD+DEwyzxRJ8nnujzxOr0vUfD4TBPPPEE7777Lm63\nm7Vr1/LFF1+wb98+rrjiijbdWGicokBuboQ1ayzMmlXb5GjbRx/ZyMuLtLiuW2ezGmzkJQ+gj70P\nVYEqiv3FeENezIoZyxEbt9d6jJQVWxg0pPGgtG6f0ZPHt32Be1Mjafu8e6kOV/FN+Wq+KV+N1WBj\ncPIQxqWNZ81H5aiWy9FRObAvPt2rqhexac2LnDL+hGbvF98j1hSfPo342Rn8AVmSSbdm4DK7sBlt\ncKjYiizD+PGBZq8nNE2SpPq1dLquEwwG8Pm8yLJUH8AZjUag/VPjopCwIAjdSYuCtoULF1JaWsqf\n//zn+lptJ554Ig8++KAI2jrB5Mk+1qyxsGaNhcmTjx5ZWbnSxltvJXP66f5uE7TVMcomMm1ZZNgy\n8IRqKfUVUx2qPjR1akWRFDasSefzlTn87t51qEdsHn/4PqPJKR1f3mJW7oWMdY3nB892fqjZjjtc\nzYaqdQx3jMBdacRkMpKZ4ycSVrAnhTGpGoqx5Q9uSZLqN7CP6TEq/OWU+oqxGCxk2/qQojqazXD1\n+aSE7MTRU0iShMlUl6WrEQgE8Hpbl4jTnNpaC35/FJvNjsViwWhsXwa1IAhCe7QoaFu5ciUffvgh\nVqu1fvohMzOT0tLSY5wptEVeXoTc3AirVlmZNMnfYLH6p59aWbYsmfz8ABdfXNN1jTwGCZkUNYUU\nNYVA1E9loIISXwk6OmnZVnQ9h5JCK/0HNnzAbmvjPqMtJUsy/ey59LPnclb2OZQHy9jp2UGurT9b\nXNvYtztEUjJAPGD02tdgTW1bEKBISv3uC6FYiN01u5GRSLdmkG5Nx2qwNXh/TY3MwoXpjBsXYNYs\nD8a2zS73WpIk1wdwHcVmsxII1OLxuHG7q5FlGbvdjsVixWTq+OlYQRCE5rQoaDMajUdNE1RVVeFw\nOFp8I7fbzZ133smBAwcwmUz079+fe++9F6fTyZQpUzCbzZhM8Z9i77jjDiZOnNi6T9KDSBJMmuTj\n5Zcd7Nplqh9N++ILK0uWpDB6dJArr3SToAS6drMYrPRNyiXLloM7VI3Wt5SIFmHvPgO5AxquPTOp\nGoNHuNu8z2hrSJJEhiWTDEu8Xt3kc3LZ88NSPDUXIskqUbmc8qF/ZPMAM8HdWxnqGM6QlKHYjgi2\nWtGX7VgAACAASURBVEJVVFRFJabHqAxUUOYvwWqwkW3PIUV1oEgKFovGmDEB/vMfG1u3qlx5pZv+\n/bu+mG5vpygKihKf4tc0Da/Xi8fjqa9VV7eeLlEZrYIg9F4tSkRYtGgRBQUF/PGPf+Siiy7i3Xff\nZeHChfTv35/bbrutRTeqqalhx44djBs3DoCHHnoIj8fDggULmDJlCs888wyDBg1q8wfpKYkIdSIR\nePT/s/fm8XXV553/++zL3aUrybJsY2zwxmLALE1oIKE4hD2mkAUSoJkkzY9CW5o0TUler8nQZQaY\naZqEkpLOTEsyDKRJWMNAISEhTZqwgwHbeN+16+7L2X9/XOnawpItyVfXknzeeeWF79FZvvfo6JzP\neb7P83z+LkBRfg34RKMBr79+MaefHuVzn8twrHuOHl1SfMBXvpqipXOAD137CgICsqigigqyqBzT\n6ad8Ns8vn9tNdkhBaR2gsmoT+539w/3pQEBgZXIV60649qiPZXlVKm4VAYGOSAdpI40hR9i0SeX/\n/J8kuZzIJZcUOe+8PTz99HoKBYVYzJnVHqazjcNd50EQ4DgOnldzBtE0vd6SRAnDpFMmTIpvPuE5\nby7TXohw++23c88993DVVVdRqVS45JJLuO666/ijP/qjCR8okUjUBRvAGWecwcMPP1z/PJcEVyMo\nFjNks6P7fMnyY/z+75+GLM/2B7bAyUtg5875nJY+g6Kdp+iWKNqFegNfYTiJXBYVlOH/N0PMxZNx\nrrhuxJptOXA+FbfMlvxmNmY3sqO4DV1qjFG6JtX623mBR1+pj55SNxE5yrzFnfzFX1Z59McpnnzS\n5rnn1mPb69A0E8sqzwkP07lALZ9OBWoFEZ7nMjg4ANRmJ8I8uJCQkEYz6ZYfQ0NDpFKpo7oJBUHA\nZz7zGS6++GJuuOEGLrroIuLxOEEQsGbNGm6//XZisdgh2+XzefL50RWHkiTR2dk55yJt3/veC/zm\nN+sOcWl43/se5cYbx3YHaCZH237ipZcMtm1T+djHcqOmeQN8bM/B9qpYnk3RKVK2S5SH22lArSaw\n5geqIotyQ/rCTZSqV8XxHWLKodfnxuwGsnaG5YmVtGgtU9r/SPRNFEQ6zA5+/MBWNr1zLaKooSgS\njuPNqOtgrjPV69zzPFzXxvcDRFGq58FpmhYKuCMQRn2aT3jOm8tIpK27u/uQ1LN4PE48PnZvUDhM\npG3Pnj3jblQqHfC1XLhw4WTGCsCdd95JJBLhhhtuAOChhx6io6MDx3H4m7/5G+68807uueeeQ7Z7\n4IEHuPfee0ct6+rq4vnnn8cwRGRZnjN5JYWCgqa914bJpFhUSKWOzp6pURzNOC65BGrJ/hPbRxAE\n2J6N7dlU3SpFu0jBLlB2yngHiXVVUtFlfdqEXIzxnR/W736Nnfmd/LLv53RGOjml9RRObTmVtDFx\nk/uR/XuBR9nJM1DKYuOiiwogoigSM+06mOsc7Xn2fR/btqlWs7iuTDKZJBKJDEfpQsaire3Ql6KQ\n6SU8583nhhtuYN++faOW3Xrrrdx2223jbjOuaFu7di2CIBw2eiUIAhs3bpzUIO+66y52797N/fff\nX1/W0VFLBFcUheuvv55bbrllzG1vuukm1q1bN2rZiEgTBI3+/gy+7yFJ0qyfkojFHCyrfEikLRp1\nZkSD1UY2eg2CWlPhieXpSchESBIhqXaAOiLmavZaWStLd36AIKjloKnDBQDNiMadmTgHLTDZkt/M\nnvxe9uT38syOf+MPTv4s882uKexRoSUVsHNLmapjo8gSQiAj4xOJWjPiOpjrNLahsUC1ajM0tJcg\nCNA0jVgsjq4bc+ZlsxGEUZ/mE57z5jISaXvwwQfHjLQdjnEfk5s2bWrM6A7iG9/4Bhs2bOC73/0u\n8vATulKp4Hke0WgtKe+pp55i5cqVY25/uLBhLBbHNKNYVpVisViPBiqKUj/WbOLKK09n48ZHDvFD\nvfLK1cd6aA3n7bc1HnoowW23DdHZ6U5yawFV0lAljSgMG97X/EFLTplsdYislYPhqVVd1lHF6Zmi\nWpZYzrLEchzfYWdxB5uyG9lf3k+nMX/K+6xVtD5GPncNkqhhWQUc4QkK0hK2Z7fRaqSJqtExnRdC\nZh6iKKHrtZxI13UYGOhHEAQikWi9CnU2v2yGhIRMnM7OzklvM6mctt7eXnp7e+no6KhHxybK1q1b\nufLKK1m8eDGaVoseLVy4kC9/+cv88R//Mb7v4/s+S5cu5Wtf+xrp9MSnlAAGB4v4/oGv4nkelUqZ\nQiGPbVuIooiizK6+SjPJD/W9NDICcd99KfbuVbjzzr5pqYr1A4+KW6HklBiqDlK0CwSAiIAuG6jS\n9E1TjWenlbdz/N/t/4cViVWsTK6kXe8Y92E9UtFaLuiYsSqF/AfYtnkJF121mVVn70EAknoLab0m\n4GQxrFxsFM2wDguCANu28X0PWZaIxRIYhnncVqCGUZ/mE57z5jLt3qP79+/nS1/6Em+88QaJRIJc\nLsfq1av57//9v9PVNZVpn8bzXtF2MI5jUyqVKBTy+L4/J6ZPjzWNeJhlMhl+8IO3eOaZCKeeavPF\nL65oiij1Ao+KU6JgFxmqDg57htaa4eqSPmXP1Mnwcv+LPLv/mfrnFrWVFcmVnJI8jXajfcxtYjGd\nQqGK5wr86PtL2bopyRXX7eC0Nf1U3Qq27yAACS1Jq5EmpsZQxDBv6mhott+r53k4jo3v+xiGQSyW\nQNf1WfWyebSEAqL5hOe8uUy7aPv0pz/NihUruP322zFNk1KpxDe/+U02btzI97///SkduNEcTrSN\nEAQBllWlUChQLpcQBJBldVZOnx5rjvZhlslk+K//9U1++9tPADrLl+dJp49NKwvXdyi7ZfJ2nkx1\nEMu1CABFlNElHekwtlNTxfM9dpd2sTG7gXdzGyl7tXN5Xtv7uHj+h8fcZkS0Qc3u64cPnMzOrXGu\n+vh2Tj1zCKhd41WviuVZCEBUidJmdhBVY2hSY90CjgeaLdoOxnEcXNdBEASi0dr0qarO/enTUEA0\nn/CcN5dpF21nnXUWL7744qhwvW3bnHfeebz++utTOnCjmYhoO5jR06c2oihMaPp05HTV/htQ+1j7\n74FlI+tM7bu8l5q4VGbU2/bRPsy+970X+I//WMeGDXEUJWDFCnvGtLKwPYuyWyFbHSJTzeAGDgIC\nulzrq9ZovMBjT3E3m3IbWd1yBp3moTlwJbdER7KFYtGqL3NskR/8y8n07jO55S/WY5ijE1qDIMD2\nLapulYAAU47QbrYTU+PocmN6zc11jqVoGyEI/OHpUx9ZVojFYkQi0TlbvBAKiOYTnvPmMu3Ndc84\n4wzWr1/PmjVr6svefvttzjzzzCkddCYgSRLRaIxoNIZt25TLtenTIAiG85BGi66RSlpBqHkciqIA\niIhi7bMkiQiCUP9Z7d+NeSP2fZ9SqYTv+4iihKoqCE3sTTYdDAwISJLG0qU2qlo70aKoMTh47KMI\nI4UNSS3JCQmfiluhaBcZrPSTs7K1KJwgo8uNicJJgsTi2Iksjp047jo/2P5/cQSLJebJLEssZ2Fk\nEYoKH7tpC4MD+iGCDWrX7EgDX6j5n+7K7yQgQJd1UnorcTWOKUcOa2IfcmwRBBFNG24F43lksxny\n+RzpdFu9qCEkJOT4YEJ36oULF/L5z3+eD37wg8ybN4+enh5eeOEFrrjiCr75zW/W1/uTP/mTaRvo\ndKKqKqqqEo8ncF132KB9RHgd/O/GCbHJkkq1YllVyuUSpVItqjibc/PS6YAtWyxMc3RLk9bWmdUg\nWUDElCPDUaoOXN+h5JTJWENkKkOjonDTVZVqeVUKToFqUOal8m95aeC3mHKEZfHlfLjrI3R2+RPa\nz4j/KYDjOfSVeukp7icgIKpESemtRNUopmwihtWoM5IRH1TPc+np6SYej5NIpOZs1C0kJGQ0ExJt\ntm3z4Q/X8myGhoZQVZW1a9diWRY9PT3TOsBmIorijG14KQgCum6g6wbJZAu2bVEsFimXSwSBjyQp\nKMqx9e2cDLO1pYksKiS0BAktweL4YipueTgKN0DezjU8Cgc1u6s/XnU7WaGfV/e/wbu5TWTtDDuL\nO5CFqR1DkZR6wUVtGtVmX3EPfhDUixlSegsRxcSQTWB2XFfHC5IkYxgSxWKRSqVKOp2uR+NCQkLm\nLpO2sZqpTDanba7g+369N125XAYCZLnWm246BVyjqkdnakuTqeD6LmW3RNbKMlgeqEfhalOURx+F\nGylECIKA/mofRbfIktjSQ9bLWhm2DO3h1LaThgXX5PADH9uzsbxaLpwkyCS1FCk9halEjquChpmQ\n03YkXNfBcWwSiRTxeGJG5b5OhTC/qvmE57y5THshAtSa4O7atWtYGBzgrLPOmtKBG83xKtoOxvM8\nLMuiWCxQqdR+T9Ml4GbDw+zYEtR7ww1WBijYNc9cSZAwZGNKUbiDq0cPxw9feZWnt/87XQsrLG/v\nYnliBcvjy4mriUkfE8DzXaqeheM7QIAiabToLSTUJBHFnNN94WbLdR4EAdVqFUVRSKfTqOrsFdah\ngGg+4TlvLtNeiPDYY49x5513oigKun4gBC8IAr/4xS+mdOCQxiNJEqZpYpomnudRrVYoFgtUq5Ww\nvUnTETDk2tRi2mgbNwo3HblwS+fHSW1ayf7dm0HYza7iDp7d9zQf6bqcNemzJ70/SZSJHCQyXd9l\nsNxPX6mHgICYEqPN7CCmxlCPoyjcTEIQBAzDwHEc9u/fRyrVQjyemDXpEiEhIRNjQk/we+65h29/\n+9ucf/750z2ekAYhSVLdGsd13bqAG4nAKUoo4JqJLMrE1QRxNcGi2KLhitQCg9XBhufCnTX/ZE66\nYhX//N2FDOx7m/kXP0Mfm+iKLGjYd4mqB8ylLa/K9tw2ICCmxmkfFnBhY9/mU7Ptk8hkhiiXy6TT\nbcets0JIyFxkQk8HRVE499xzp3ssIdOELMv19iau61CpVCkW81QqZQRBQFEUJCkUcM3jQBSuzezA\n9V1KTomcfXAUTkSXtSlH4eJJh5s+t5fv/+PvkHn0/Xzqs2/RoY/t6/rDHT+g3WhnZWIVbXr7pI83\n0lYkCAIsz2JbdisQkFCTpM024mp8Tk+hzjQEQcQ0I9i2RXf3Xlpa0kQi0TDqFhIyB5C+/vWvf/1I\nKyUSCR555BFOO+00DGNm9gWqVOyGNbOdy4iihKZpxGJxIpEosixj2xa2bQ23OxEnlMhsGArVqtOE\nEc99REFEl3USWpLOaCcteiumbGC5tVYfllfF810MQ8OxJ9beA0A3PE5emWXLxhTLVhaJJw/9fQ1U\n+3l2/9PsLu3itcFXeCf7NiWniCEbRJXJ5VwIgoAsyvUmxFWvSl+ln95SNyWnhCRIyKI8q9qJzObr\nXJJkRFEin8/hODaapiGKM//cRyIa5bJ9rIdxXBGe8+YiCAKmObWZiAkVIrz++uv82Z/92aj2HiNG\n2Bs3bpzSgRtNWIhwdDiOTblcplgs4rrOsEOEOu5NfrYkaM92Du4L58plMvnCpKNwvg8jOnzEfD47\nqJBsdTj/4i4y8hCbshvYlNtEZdhOK62184cr/r+GfIf3Wmsl9SRpvZ2oGpvxTX3nynVuWRZB4NPa\nmsY0IzM66hYmxTef8Jw3l2mvHl27di2XX345l1122ahCBIBFixZN6cCNJhRtjSEIAhzHoVIpUyzm\ncV0PQaj1rzs4AjdXHmaziWTSoHtggKJdZKg6RMHOEwCyIKHLxhEFUD6b51/u7SWfuwZB1Ah8i3ji\nEW6+tYN4Mo4XeOwu1vxQW/U057X9ziH7cHwHWZh6NXJNwFWwPHtYwLWQNtqIqTGkGRiBm0vXue97\nVKtVIpEoLS0tMzYlIhQQzSc8581l2kXbOeecw0svvTSj385C0dZ4giDAtu26R2vNRktEUVRaW6Nz\n5mE2W3ivgBipSM1bOQarg9ieBQhokoom6YjvsTr7yQ/f5o2XPokgHqjwDHyLM859iCuuO3VCY/hF\n9/O8nXmLFcmVrEyewnxj/pTvC37gU3Ur2H6tkrZFbyWlpzBkE12eGY1i55JoG8Gyam1jRqJuM41Q\nQDSf8Jw3l2lv+XHNNdfw+OOP89GPfnRKBwmZnQiCgKZpaJpGIpHEti3K5RLFYpFSqUSlUkUQakI5\nCIRhX1ahvu2I/dfI54MtwQ4sm7kvAjOdgytSF8QWUXWrlJwiGWuQbDVHQICIgC4bqJJKdlCpC7Zi\nXkE3PWRZIzs08SKBPaXd5JwsL/b/hhf7f0NcSbAisZJz2s4jqSYnNX5REDGVCCY1AVewcwxWBwBQ\nJLXeC85UjLAStYFomo7nefT19dZzW98bSQ8JCZmZTEi0rV+/ngcffJDvfOc7pNPpUT978MEHp2Vg\nITOLmoDT0TSdZLKFWExB0/IEQUAQBMNRzgDf94c/+wf9zCcI/OF1fDyv5uQAQX25YRgIQvjQOBp0\nWUeXdVqNNH7gUXbLFKwCg9Wa0b2eyON6ZcCkt9tEln26Fg2SbJl4ov0NS29kb2kPm3Ib2ZjdQN7J\n8dLAbzmrdc1Rjf1gAQe1KOJQeYDeUg/C8Hdr0dPE1CimEp2RU6mzCUmSMAxz+CWsgCgKGEaESCSC\nqmqhl2lIyAxlQqLtYx/7GB/72Memeywhs4SRRp6GMXYLicmSy2XJZIZm5FTNbEUUJKJKjKgSozM6\nH9uzSK9r5++2PcFg9krauwJ69upkh57lnPOXTGK/IouiJ7AoegJr51/C3vJe9hR30aqnD1k3CAJ2\nFXeyMLIIaZJVi7IoI6sHpg8cz6a7uJ99+Agw2uBeMREIBf9kGXkRAwgCn2q1QqlUAEQMw8A0TXRd\nR5bDdi0hITOF0Hs0ZEo0MgciCAL6+3uxbQtVnRm5TDORxvm9vkFPv0/JrrJ124W0d+p8+nNbiMUa\nK3y6y/v531v+CV0yWBZfzvLECk6MLUE5yp5tNYN7i6o7YuklkNQTpLRWTMXEkA0aZXA/F3PajkQQ\nBLiui+c5BAGoqkokEkXXDRRFmfaUhjC/qvmE57y5NMV7dGBggPXr15PJZDh4k2uvvXZKB240oWhr\nLo3+I3ddl56e/UiSNGOr2o410yEg3nxb5L7vJGhb1MvVN72OJqnoktGQB/OOwnae3fcMA1Z/fZkq\napzX9jtcMO+D9WXvbUNywdpFxJPxCR/HD3wsz8L2LAICZEEhoSVJaAkMxUCX9Cn3hjseRdt7cV0X\n1631wZRliUgkhmEYqGpj7ddGCAVE8wnPeXOZ9kKEn/70p/z5n/85J5xwAlu3buWkk05iy5YtnHXW\nWTNGtIXMbmRZJp1uo6enG8MQw/y2JrH6VJ9bv1AmkTBItqygt9xDtppBFEQicuSoLLVOjC3hD1fc\nwkB1gHeHc+B6qz2jIm0H2pDUqlp3brPY/u4j3HwrExZuoiBiyMZwhK1mcF+wcwxVBwioxdwiSpSE\nliSiRDFkPfRInQSyLNct73zfI5/Pk81mkKSa84Jp1goZwjy4kJDpZ0J35L//+7/nb//2b7n00ks5\n55xzeOyxx/jxj3/M1q1bp3t8IccRum6QSrWE+W1N5rTTrOF/1SpRq26VTHWQ7lI3buBiSMZRteBI\n62nS+gc4v+MDDFlDaAcJpl8+t5t87pP09aYopH9BqtXCK6zll8/9ZMJtSN6LJMqYB4nN2nRqLScu\nwG94NO54QhQldL12noLAp1KpUCwWAQFVlQERURTqziojFeIH/7v2M+Gg6vEDleeCIGDbWr15e0hI\nyGgmJNr279/PpZdeOmrZunXrOP/88/mLv/iLaRlYyPFJPJ6gWq1i29Uwv+0Yocs6ndEuOiLzyFt5\nukv7yVgZJCQiauSoKjdbtJZRn0fakETjFj2Lf0TRHKB3oU8Fh47+EssSK0ioiaP6PoIgoEnaKLE4\nXjQuqSWJqFF0KYzGHYla0+3aORqpEocAzwsIAq++vFYlHtQ/BwHvaRU08u/a76pSyZLPV4lGY5im\nOW3TsCEhs5EJibbW1lYGBgZIp9N0dXXx+uuvk0qlhv9IQ0IahyAItLam6e7eh+e5YX7bMURAIqmn\nSOopKm6J/soAfaVefAJM2RglgqZKstVh5zYLMyqxsHwpffYbVONv06Ps56mdz/Kc+m/8ySlfJCI3\nNvI6XjRu/0HROEVUWRjMQ7A0zHrD31A8jIUgCA2bHjVNk0rFp1gskM/nEEWJWKwm4BRFDQVcyHHN\nhJ6I1113Ha+++iqXXHIJN998MzfeeCOiKPIHf/AHEz5QNpvly1/+Mnv27EFVVU444QT+y3/5L6RS\nKXbu3MlXvvIVstksyWSSu+++e8bYY4U0H1mWaWtrH85vk8Kb9DHgV78y2bBB4zOfySDLYMgRFsUi\nzI90kbOydJf2kbEyqIKCoZiHuC+MRxCA7wlIci26csHaRWx/9xHyuWtoyXyIlP9+3L4fU21NIuhv\nsej0fWMKtpHITaOujfGicblqjsFcHgBZkIlriWHXBqOhVaohoxFFsd6OxPd98vk8uVwWWZaIRuMY\nhtmUStaQkJnGlFp+7N+/n0qlwtKlSye8TS6XY/PmzZxzzjkA3H333eTzef76r/+am266ieuuu44r\nrriCJ554gh//+Mc88MADkxpTWD3aXJpRbZTNZshmM2F+2zDNrGR84QWTf/3XBGedVeHmm7McGkQJ\nKDpF+st9DFYGhyNTMrpsjDt9WirI/L9HFmNGXC6/dmd9eb16dEgh2VKrHvX9NJIcEI3ZYz6YdxV3\n8tiuR1ieWMHyxAoWRU6YdC+4iRCL6RQKtdYinu9ieRaO7xBQK4BIaimSWrLhrUaOZw53nXueh+va\n+H6AoihEo7G6gAuZOmH1aHOZ9urRg9m+fTvbtm1j5cqVk9oukUjUBRvAGWecwcMPP8zQ0BAbN27k\n8ssvB+CKK67gr/7qr8hkMqRSqckOL2QOkUgksSwLy6rW37pDmsOFF5ZxXYFHHokjSXDjjVlGuxwJ\ntea9iRiL4ospOUWGKoMMVgfxAx9ZkDBko159uumtFE8/egKWJfGhj+wdzl+q7SmejI9RdGDXjzMW\nO4s7KLoFXh18mVcHX0YXdU5KLOPMlrNYFD2hkaeiznunVL3Ao+QUyFRrolUUJBJakpSWCkXcNFFr\nCTRcJex5ZLMZMpkhFEUhFkug63oo4ELmNIcVbf/tv/03Vq5cydVXXw3AY489xh133EE8HqdcLvPt\nb3+bCy+8cNIHDYKAhx56iIsvvpju7m46Ojrqb9OiKNLe3k5PT88hoi2fz5PP50ctkySJzs7OSY8h\nZOYT5rcdW37v90q4LjzxRBxJCvjUp3KMNRslCVLdA3VR/IRh/9MsA+V+ymV44anlbH6zk84FFa7+\n+HbSHdVDdzJBCnkFRfG5oOODLIsv593cJt7NbWLA6uftzHrmm13TJtreiyRIGLKJIdfMt7zAo+wU\nyVaHxhBxBrpshM4NDWS0gHPJZAYJggBN04hGY+i6UW9VEhIyE+nu7sbzvFHL4vE48fj47Y4Oe0X/\n9Kc/5cYbb6x//ru/+zu++tWvcsMNN/Doo4/yD//wD1MSbXfeeSeRSIQbbriBd955Z8LbPfDAA9x7\n772jlnV1dfH8889POdQYMnXa2mJNOU4iobF3714ikcY0fZ3NpFLmkVdqIJ/4RICm2fzsZxF83yOd\nPnLxUSsxFtFJEKzggQdF9ryrccGlOzjvop0osoChRpCn2P/tR99bwkCvxrrr97BshcGyjiVcyWUM\nVAbYMLSB1W2riY1Rdfzbnt+iiApLE0tJapMzto/FJhPlPTCVP9L0t9/dBx5IokSb2UaL0UJUC/1T\nD8fRXOeO4+A4ZYrFEoZhkEgkMIxQwB2JZt3PQw5www03sG/fvlHLbr31Vm677bZxtzlsTttZZ53F\na6+9BsDmzZu59tpreeWVV1BVFc/zeN/73sdLL700qUHeddddbN68mfvvvx9ZlhkaGuIjH/kIL774\nIoIg4Ps+5513Hs8+++ykIm1hTltzaXYORDabIZfLYhjNFS0ziWPVnT8IIJ8XSSQmXy1eqQj09cmc\ncIJN2S2Tq2bpq/RhexYCAqZsokjqhPe3b3eEJ/71RIb6dc5+fx8XXboXRT38uIIg4O83/A/KbgmA\nFrWVE2NLWBw9kaXxkw5rq3VwTtvR4vkuVbeKE7gIw9ZbrXobUTWKIk78HMx1Gnmdu66D47hAgK4b\nxGIxNE0PGwG/hzCnrbmM5LQ1PNIWi8XqrT5eeeUVTj31VFS1dnNxXZfJ1jB84xvfYMOGDXz3u9+t\nv/W0tLSwYsUKnnzySa666iqefPJJVq1aNWY+25G+TMjcpZbfVsWyLDQt7J/VTASBKQk2AMMIOOEE\nBxAw5QhmNEJndD4Vt0zOytNf6aVkZRAQ0WX9iG1EuhaV+OyfvMPPn17Ay7/uYPvmOFd9fAddi0rj\nbuMHPh/ouJAdhW3sKu5iyB5kaHCQ1wdf489O/fMpfa+pIIkyETVaH1PZKZOpbkEAokqUtNlGVIkf\nVSPjkNHIsoIsK3U/1f7+PkDANA0ikRiapoUCLuSYMZXUrsOKtksvvZTbb7+dtWvX8s///M987nOf\nq//szTffZOHChRM+0NatW/nud7/L4sWL+fjHPw7AwoUL+fa3v83Xv/51vvKVr3DfffeRSCS46667\nJv1FQuY2B/Lb9of5bTMQ161F41paJiLuBAw5giFHmBfppOpWKNh5+sp9ZK3M8M91VHHspqqKEvDh\nq/awbFWWJ394Iju3xQ4r2iRR4uz0OZydPgcv8Ogpd7OjuJ2yWx5TJFqexeuDr7I4toToNOXH1ay3\navlwtR5xFjtzOwgI0GWdtN5OQk9gyiZhMcPRIwgCiqKgKDUBZ9s25XIPgiBiGCbRaE3AiWKYcxgy\nszns9KjjONx///28/fbbrF69mi984Qv1m+gDDzyArut1AXasCadHm8uxCqdXKhV6e7sxDPO4q4d2\nHQAAIABJREFUy2+bSeblmUyG73//bVw3QFUFBgYuQJZb+cu/HBijPcjEsTyLol2gv9JHwc4TIKAf\nxsTeqoooql+vbD1a83mALfnN/OuOhwBI6HG69EUsjS3lxNhSYsr05/04nk3FqwxX4Sq0mmlSw76p\njbLaymQyPPnkegYGBNLpgCuvPH3GVOs38zoPggDHsfE8D1EUMM0IkUgUVT2+BFw4Pdpcjqblx5T6\ntM1EQtHWXI7lH/nxmt82U0RbJpPhq199i7ff/hiJhEo+bxOPP8pXvnI655/fuJ56jm9TtIsMVvvJ\nVrMEgCIq6LI+ZhL/AfP5axBEjcC3iCce4eZbOyYl3PaX9/HqwCvsLO6g7Bdxh3NOViVPZd0Jv9+o\nrzchPN+l4lZwAw9REElpLbQYrUQUc8p5cJlMhrvvfpOhoWuQZQ3ft0gmH+HLX149I4Tbscvd9HEc\npy7gIpEophlF0+a+jVYo2ppLU/u0hYQca2r5bZVpy2/zPBfHcWjU64wkiXPKfufJJ9fj++tIJlWy\nWZFEQmXevMvZtu1Rzj9/8tXk46GIKim9hZTeguu7lJwSmer4veBGzOcFUav1gRM18rlr+OVzD03K\nfH6+2cX8RV21aTSlxPrud9he2M6y+PIx1++t9CAg0Ka3N/x3LIkyUbUW3fMDn7ydY7A6gADoskGL\n3kpMjWLIE6vIzedFvvWtjbz++sexbYMVKyxEUSObvYYnn3yUG29s3O9vtjHaS9WnVCpRKBQQRXHG\n+aDWpngtRLF2bwk5fghFW8iso5bf1jac3+Y1JJHY8zwcxwYCZFkhkUgiNqjDvm1XKZVKBEGti7ss\nz+7mnwMDApKksWCBQ1ubgK4HgMbg4PQ9zGRRJqElSGije8ENlgdwAxcRkaFBCUHUKBVl+ntMFiwu\nIssa2aGpnW9BEEgbac5pO49z2s4bd71f9f6STbmNROUYJ8aWsCS2lBNjSxrulyoKIhHlwD4dz6a7\nuJ991Izao0qUlNZCVIthyOaoaOSLLxq89JLBu+9q7Nmj4fs6ra1uvcmxKE7v72+2IQijbbRmgg/q\nyFRuuVymUCjg+x4gMG9eZ1icdRwRiraQWYksK7S2ttHf34uuT61/m+/XhJrv14RaMpnCMIxpeHON\nkUy2UK1WKBTyVCplBEFAVdWGCcNmkk4HbNlSi9DUBBv4vkVra3PSE0RBIqYmiKkJFsYWUnbK5Kwc\n0dRW7K1FBNnEcSIM9um0z8uQbHGmdTwxJU5UjlF0C7yVeZO3Mm8CcONJn2FhZOLFWpNFkdR6u5QR\nw/t9xb34xaBWkarGaNFbiSgRXn0tyeCgxCWXFNi9u8zbbxcQxQMP+mb+/mYbx9IHtSbUHCqVMsVi\nHtf1hiOCKqKo4bouvb3dzJvXWY8ShsxtJiTaQkupkJmIaZrE4wny+dyE89t838e2bYLAR5Yl4vFk\nU8ynJUkiEokSiURxHIdyuUShkMfzLCRJmlXTp1deeTobNz5CNnsNonggJ+rKK1c3fSwCIhElSkSJ\n8vmPX8J/3fEcg5mrSLZUyQzCvAWPcP7FXdM6hg93fYS18y+hv9rPjuI2tuW30V3Zzzxj3pjr7yzs\noMPoqDspNAJBEBA9A8GKkow79YrU3fmdAKz+yLu0J6KkjBbWFJewZ++PyWV//5j//mYboiii6zUB\n53ke+XyWbDbTcB/UA0KtgOM4iKKALKsYxmhhVmudFdDb20NHR2e9JVfI3GVChQirV6/m/e9/P1df\nfTUXXXTRjLwwwkKE5jJTEld936e/vwfHccd90/R9fzii5iOKIrFY7e1YVY+tUAqCAMuqUiwWKZVq\nLStq06djv0vNlEIEOFB9ODgo0No6c6oPR8bV1yfw2us6C5es5NpbNoIQoEv6pHugTbW5rud7YxrY\nV9wyf/fOPQC0aK0sMBfSFVnAAnMh7Ub7Yfc5VmWsGU2w/d0EG9a3sHlDkuWnZLj6EzsO2XbEncH2\nLAICSvkyb/wiQyUfoyMtsu7qNSSTKYIAjlXR5MjvrlBQiMWcGXNNTYSR9IqRFIip+KA6jkO1WqVQ\nyOE4znCbEnVC6R+O4+D7HvPmdU5ppmCm3M+PF6a9enRoaIif/OQnPP744+zZs4dLLrmEq6++mrPP\nPntKB50OQtHWXGbSH7nrOuzfv2/UDS4IfGy7diOrJRJHMc3IjEkkfi+e51GtVsjncwclGI9uOzCT\nRNts4MUXDb73vSQ3fGqIFWfup6/UQ8EpICAQUaITStxvpCMCwGB1gJ/seYLuSjde4NaXJ9UUf7Ty\nj8fd7r2VsY7jYFWeIpk6H9drwzBdVpyW4dQzB1l0YvGI4/ACD9uzsLzhPE5B4xePnEl7i8wnPmY1\n3WJrpKI1m70GTTOxrPKMqmidDAcKmY7sg+q6bj1twrbtej+5qfShrB3Tp6Ojc9LRvpl0Pz8eaGrL\nj+3bt/P444/z5JNPIggCV111Fddeey1dXdM7BXEkQtHWXGbaH3m5XKavrwdZlt9Tsh9B0/QZKdTG\nw3Hs4cq1PL7v16dPW1oioWibBEEADz+c4Hd+p8yJJ9by2qpulUx1iN5yD47voIgyhmwiCmOHlxot\n2kbwfI+eag/7SnvZV95DTIlz8fwPH7Jeb6WHl/pfZN9rHvte/U9o9hIEBHxfYOdWlZWn/YB1N6xi\n8dICkjz1+5/ruzz16Hxe/20nV3/qLVaf7tKitxBVYxiywXQ3+P3e917gN79ZRyZjUqlIdHXZBIHF\n+943uytaXdfFdW2CADRNJxaLoaoatm1RKBSwrCqCALKsNsQbdSTaN1nhNtPu53Odprb8GBgYYGBg\ngFKpxKpVq+jt7WXdunV89rOf5fOf//yUBhEScrSYpkkq1YLjOESjs7s5pqKoJJNq3bqrUChQLpco\nlcD3g1n7vZqNIMAnP5kbtUyXdTqj85kXnVdr4lseYKg6QAAYso4mNcdCShIluswuuswuYOzK1CCA\n13Z084b1JvuFIpVT9iB6BnppKfGhCzhReB/zukosXZ4fc/vJIIsyl13VT/+eND9/7HQWLXqVgrmT\ngABZUEgZLSS1FFElgnwYr9apMjAgMDRk0t0tD+dvycybx6yvaJVluS7GXNdhYGAACAABRZEb3mtS\nUVRs26avr4eOjnmzvlI95FAmJNq2bNnCE088wZNPPolpmnz0ox/liSeeoKOjA4BbbrmFq666KhRt\nIceURCJ5rIfQUARBQNcNdN3A8zwMQ2Dr1t0IglCvZguZGgJivQJ1kb+InJWjp9RN1sogCRKmbNb7\nvzWTIIDeboMNb7SyYX0L/eUuVl+lIIkvsN2K4mpZyvG3MUrLIbAaWhmrKAEfvX47//tbq3j6h6u4\n/rPvIoq1Br/Z6hD95T7qrUX0VuJaHEM2EDj6l4hiUaa72yWREInHwTS9OVfROuKDOt2oqoptW/T1\n9dLePq8hEbyQmcOEfpuf+tSnuPzyy/nWt77F6aeffsjPFyxYwE033dTwwYWEhNSQJIlEIsb8+V0M\nDQ1RLpfQND00u24AsqjQaqRpNdJU3BJD1Qy9pR7cwEXSE3hB0JQcrw3rU7zwbBdD/TqiGHDiyXku\nWF1l2arVXHzSIv7l3l6GyhdRje1ALXUSTzzCBWsXjdrHCz0/Z7A6yOLYiSyOnkhKTU0qNSDdXuXD\nV+/mqR8t5vUX21jzvv6a0b14YCrH8iz2FnYTFEBEHG6AnCKiRFDH8HI9EpmMSE/PhXR2/phU6kp0\n3cSyqmFF61GgqhqWZdUjbqFX89xhQjlttm3PyIrRgwlz2ppLmAPRfEbOeRAElMslhoYGAWZsccVs\nxg88CnaRqpxj30AffuANT2rVRJ4qKsjixNrETNQPddNbKV75TTurVg+x4tQMZsQdez9DCsmWsfdz\n/6b7GLD665/jSoLF0RP53Y4LSGkTS+gPAnjzlTSnnDGIohz+nuoFHpZbxfIdBAIM2aBVTxPT4piy\nOWGv1B07FCKRPp55Zj3FokI0OruqR2cqtl1FFGU6OjoOK9zC+3lzmZZChB/96EcT2sG11147pQM3\nmlC0NZfwj7z5vPecu65LNjtEsVgMo24ToFgU+PnPI1x6aZGJzhiNVOw6vo3lWVTdKkWnSNEuUHUr\njNxxRERUSUUR5VHTqodUfdoOqvo4t/5ly6SN7CfCYHWAncUd7CzuZFdxJxWvVrhy28o/Ja4mGn68\n9+J4NhW3gk+AgEBSTw43+I2iTTAKF1ZJNxbbriJJMu3t88a9R4T38+YyLYUIjz/++BE3FgRhxoi2\nkJDjDVmWSafbMc0IQ0ODOI496yplm8muXSrPPBND1wPWri1NaltFVFFElagSI220AbVonO3ZVD2L\nilOm5BQo2MVRrTx+9sw2srkbKRWi5DMalYqMIHyKnz/9j1z9yYn7oU6UVj1Nq55mTfocgiCgt9pL\nd3nfmILNCzwe3PZ9FkQWsjS2lAXmwjF7y02Gg10a/MCn7JTIVDNAgC7rtOhpEmocU4lMOAoXBDXP\n1ETCP6qxHa+oqo5lVYZz3DrCl7tZzrii7fvf/34zxxESEjJFRtqaZLMZCoU8qqqFycdjcMopFqee\nWuXpp2Oce27lqEWAKEjosoEuGyS1A0Uwru9geRaWZ/FUboDsUILBPh1F80i2lojFbfK56X9wCoLA\nPGPeuM4MPeVu9pR2sae0i9/0/QpFVFkcXcyy+HLOaD3rqI8vCiKGbNadHxzPoafYzY5KD7rhk9QS\npIZttnTZGHc/P/xhnPXrde64ox/TDGdTpoKmGVhWlYGBXtLpULjNZsYt+zl41tT3/XH/HxIScuyR\nJInW1jTz5nUSBLVGvZNswXhc8Pu/n8d14YknYtN2DFlUiChRWvRW1CBJbkAh3SKycplPV6eArjqY\niRJZK0POylJxy3iBN23jGY92o4NPLvkU57W9j7TWjuPbbMlvZkP2nUPWtSyRbObo8poVSWFg1wK+\n/40LGNwzn7JbYUduG28NvMkb/a+zt7Cbgp075Fyce26FfF7kwQeThJf01NE0HcuyGRzsD5/ds5hx\nX8fXrFnDa6+9BsCqVasOmXIJggBBENi4ceP0jjAkJGTC6LrBvHld5PM5crksqqqGvZoOor3d4/d+\nr8Szz0b53d890HR3urj55lPYvPlHaNpVSKKG4Lt0tv0bf/jJS9FjOmWnTMYaIlfN4eMhIKBKGpqk\njdvwt1EoosKS2FKWxJZy8XzI2zm2F7YTUSKj1gsCePh/LWOQraz56K9YllzCPKNz0tPwO7fG+OH3\nTqI1XaVzfhVDNoYb99aa+/aX++gudbPP3olTAUMxiMgREvMM1l7q8/+eTPPrXxv87u9WGnYOjjd0\n3aBarTAw0E863Rb2fJyFjFuI0N3dTWdnJwD79u0bdwfH2glhhLAQobmEiavNZ7Ln3LKqDA4O4LoO\nmmaEuW7DVKsCf/VXbXzwg6Uj5rY1Iil+Ij6tAT5Vt0LJKZO1hshV8/j4CIAm6aiSOu0i7nBsezfO\nt577dzjp32jvrGDKEU6MLmFJbCknxU/GlA/fJHbPjigP/a9lJFosPvX5d4lE3XHXjcV0Mrkiju/g\n+m4t8hbAow+czr6dCf7gtndY1CViKia6bKBKCqqoDtuShdf4RKhWyxiGSWtrTbiF9/Pm0lQbq5lK\nKNqaS/hH3nymcs593yefz5HNZlAUddKehHOVSkXAMI58vzhWlYwBPhW3QskukrWy5KwcDNeq6rKO\nIjZfxD30VJHf7NhK+1n/gRA50Fbk6kXXcGrqtHG327c7wv/9n8uIxh0+/YebiMbGF2wwvnVYsSDz\nT984hcUnZ/jIdZtwPGe4SrWGIIiYsomhmERkE1XS0SQVXdYJxdyhVCplTDNCa2uajo5EeD9vIk2x\nsfrZz37Gyy+/TCaTGZUrc/fdd0/pwCEhIdOPKIokkylM02RgYIBKpYyu6wjHMGozE5iIYJsKQVCz\nzzpaBERMOYIpR2gzO/ADrybinBKZ6hAFu0CAP7ymiCar0y7kPnZJjMp9n2To2Zu49pYX6BPeZXth\nKyfGloy5/sv9LxJRogSVU0mkbD7xmc1HFGyHIxpz+fQfvkuq1UKSTYz3PL38wMf1XbLVDAN+37DE\nrdlwtRitJLUUEcWcFhuu2YhhmJTLJQQB2tsb334mZHqYkGi79957efjhh7nssst45pln+PjHP85P\nfvITLrvssukeX0hISANQVY158zopFPJksxlEUWzYdKkkSWHHdeD113VefVXnppuyNDqgKQoSESVK\nRInSbnYQ4GO51nC7kRJ5O0/RKeIHHjUhV8uNUySlYW4Oklyzufqf3zyF3neXc94HkpzbNrZvqud7\nPN/9M9zAAX5Ey0da+VX+BBb5J7AyccqUW4ukOw6NwI0gCrVeeao0umDC810ylUH6y70ARJQILXqa\nmBZrmA3XbMUwTEqlEn19fdh2Y+4HoiiiKGqYjjFNTGh69EMf+hD3338/y5Yt4+yzz+aVV15h/fr1\n3HffffzjP/5jM8Z5RMLp0eYSTo82n0adc8exKRaLDasurVYruK5DzQRbnVPtBCY6PfrWWxr/9E8p\nFi1yuO22ITTtWNyLAqpurdVIxSlRcAoU7EK9GlMAVElDFZWj8lXNZxXiycMXcFiexSsDL7GruJO9\n5b04vg2AKmr82al/flghOd70aCMIggDbrzVJhpoYTmopWvQWTMWckg3XbCcIAgxDJJudXO/C8fcH\noigRi8UwTTMUcGMw7dOj+XyeZcuWAaAoCo7jcPrpp/Pyyy9P6aAhISHHDkVRSaVaGrpPx7GpVCoU\nCgVs20IUawJOPMpmrc2it1eio2NqbTfeeacm2BYscLnllmMl2AAEdFlHl3USWoJad7YAy7OxvCpl\np0zRyVOwDjQAFgQBXTIOiU4djiMJNgBN0ji/4wOc3/EBPN+jp9LN7tIuHN8ZU7Dl7Rw/6/4pJ0QX\nc4q8HDWITMuDXhAENElHk3Sg1mA4b+cYrA4gUMsXbNXbiGmxSdlwzWYEQcAwDKrVxl23tVzaPLlc\nBlmWiUbjGIaJokzM+i1kfCYk2hYtWsSWLVs4+eSTOfnkk3nooYeIx+MkEhO3Rbnrrrt49tln2bdv\nHz/5yU846aSTALjooovQdR1VranxL33pS5x//vlT+zYhISHHhFqRg0osFsdxHCqVMsViHsuqIggS\nqqrO2PYC77yjcd99LXzhC0Ocdpo1qW03bVL5p39K0dnpcuutgzOw+auANtxCpOaKUOsIYHsWllel\n5JQZqPSRtTIIiBjy5ATce8kMagz265y0IldfJokSXZEFdEUWjLvdruIuNmTfZkP2bZ7rfpqIGOOk\n+MmsSKxkcezEcberlCV2bI2z6vTMlMYrCdKoFieOZ7O/uBe/OGLDlaBFT2PKkeGChpCJIIoiuj4s\njD2PfD47XAylEI3GMAwDRZnZfuYzlQmJtj/90z8lm80C8MUvfpEvfelLlMtl/vN//s8TPtDatWu5\n+eabuf7660ctFwSBb3/72yxdunQSww4JCZmJCIKAqqqoqko8nsC2bSqVMoVCHt/36/kuM0nALV9u\n0d7u8sgjcVau7J+wLynAz38eoa3N5bbbZqJgGx9V0lAljZiaYF6kk6pbIW/n6Sv3DAs4AV02JuQX\nOmJk37tfY8eWJMnWs/jjOwqo2sQbuC6KnsBHui5jV3EX+6zd5KpZXh2szeQcTrT9+vn5vPSrDiLR\nTZywpDjh443HoTZcZTLVrUAtepg22ohrcSJK5LjOhZsMtZzXWj8+z/PIZjNkMoP1lzxdN8Kq9kkw\nodvThRdeWP/36tWree655yZ9oLPOqtmivDePJgiCsHN7SMgcRBAENE1D0zQSiSS2bVEulygWi8MC\nTkJVlWNeySrLcO21ee67r4Wf/zwyKV/S//SfMliWSDQ6u+9hI3Zc7WYHVbdKwc7RV+47SMAdmFI8\nmHw2zz/eM0Bf783ksnE81yae+B7VShpVm3hFYkJNsCZ9DmvS5xCJqmzu28H2/FYWR8cWbNvyW3ED\nl/MustmyMcHjDy3hc7e/g2E2zlliLBuu7uJ+9hX3IiKS0ltoMVqJKpGwInWCjBZwLpnMEEEQoKoj\nAk4Pm4EfgQmJtq1bt/LKK6+Qy+VIJBKcffbZ9enNRvClL32JIAhYs2YNt99+O7HY2BYz+XyefD4/\napkkSfUmwCEhITOTmoDT0TSdZLIFy7Iol4uUSrUCIkmSjmnC8lR9SVUVVHVuWQKN5MW1HSTg+sv9\nYwq4Xz63m13bP0upFEUUA7oWOdj21fzyuYe44rpTp3R8URDpMrvoMsdv3P4ffb9id2kXIhKptUvY\n84sP8fAjJ3LT9S6iOD3XkCIpKFJNUBycCwcBMSVGq5EmqsaGXR7CvK0jIUlyvercdV2GhgYIgprd\nVjQaxTCMOV+V3t3djeeNftGIx+PE4+O/8Bz2jARBwB133MFjjz3GvHnzaG9vp7e3l76+Pq6++mr+\n9m//9qhvsg899BAdHR04jsPf/M3fcOedd3LPPfeMue4DDzzAvffeO2pZV1cXzz///JQrMUKmTlvb\n9Pk3hozN3Drnbfi+T7VapVAoUCgUGhZ1H7kv1Wy8Jnbj/8xnHL76VZNf/KKFm28+UDGaSh2+2//c\nxqSTFpZxIpZrkbfy9BR7KNgFBATyOYX5iwL6uh1SrTaGGQAG5YJOLDb1HLAjbXtq+yrkjMie4h5y\nwXbEM/fyyx6dpa/9EZd/KHLYbRvHgeNYrsWg28NAtRtVUmmPtJPSU0TUyDF1spgMM+U6dxwHxylT\nKJQwTZN4PI5pmnOqKn2EG2644RDHqVtvvZXbbrtt3G0Oezf7wQ9+wEsvvcQPfvADTj/99Pry9evX\n88UvfpGHH36YT37yk0c16I6ODqBWlXr99ddzyy23jLvuTTfdxLp160YtG/lFhi0/mkvY8qP5zOVz\nLoom8bjRsP25rku1WiWTyeE4DoJw5HYkmgaf/rTDSSfZZDK1e8nBLT/6+yWSSa/hPdhmEzIRFqhL\nsSWLgl0gGtuM7eVIdVQRBRHHESGwMWPVKbftmEjLjzPj53Jm/FwqboUdxe1si2/l3zNlnP6FFAr7\nD1k/Z+dIqBMvnJsKEjWhaVsuW/I78YJtiIJIQkuS1tNE1AiKODOT74+V88fhCAIolfJ0dw8CYJom\nkUgMTdNmvYAbafnx4IMPjhlpOxyHFW2PP/44X/va10YJNoDTTz+dO+64g/vvv/+oRFulUsHzPKLR\nWpTsqaeeYuXKleOuf6SwYUhIyOylkVOjiqKgKAqxWOygatYClcrh25GsXj129Whvr8Q3vtHKqlUW\nN96YG3Od4wlV0mg1ND7z8Yvp2/FTBjNX4yLgemWi8R9xxoVJclYWRVRQJW3YF7TxGLLBquQprEqe\nwmVdIEmHCrasneUfNn6TtNbGyYnlLIsvo8tcMG1T8bIoE1NrEXE/8CnZBTLVISAgIkdpMVpRJAXh\noP8hCIiCgAD1zwK1ZYysg4BQX6/2WRYl5upUbO1Fq/Z3HATBcFFTLyBgGCbRaE3AzaSipskyldSu\nwzbXPffcc3n++efroupgisUiH/rQhybcq+2v//qvee655xgcHCSZTJJKpfjOd77Dbbfdhu/7+L7P\n0qVL+drXvkY6nZ70Fwkjbc1lLkd9ZirhOT86giAY1Y7EdT0EQRyzHcmIyXuhoCBJLtu2fQhRTPOn\nfzpIZ+fUrZjmIiPnanBQoLU14NLLV2LEjVo+nJWn4BSwvOqw0KiJmprB+9g9uxrRXHekojU7qOC2\n76Bn8St40oGIhilHWNN6NhfM++BRHWeyWJ6F5VZHeaYG1GTXyH9rjCw5wMGfirkiv/1ZN4WMwYJ5\nGtdcfTbz0vOmPK6ZGGkbj5G/Y89zEQSBSCRCJBJFVWePgJs2w/g1a9bw6quvjrvxkX7eTELR1lxC\nAdF8wnPeOGo3fptyuUyhUMD3vXo7klwux913v0k2ew2CYPLuuw6m+Rh33XUqq1bNpZzC5uH6bt2J\noGAXKNh5qm6FYFiqyIKEIqmooko8bhyVaMtn8/zLvb3kc9cgiBqBbxFN/JCLP+OyP9jL5ty75Jws\nv9P2fn5v/trGfckmcfD3CwQV1y8Ti/+IP/yThZw0fxkxNTbpdiSzSbQdzMjfsed5iKJAJBLFNKNo\nmjajm/hOmyOC67r89re/HTc5+L1zsSEhISGzgVo/OQ1VPbgdSW0K9ZFHXmVo6FoEQWX7dhnfl0mn\nr+CVVx5h1aoLj7zzkEOQRRlZlDHlCC16KwB+4GF5VSzXpugWKVh58nYev2pRtKqow02BJ5vI/8vn\ndpPPfRJB1HAdEVnRKOauY+evH+KK6z7C2vmX0F/tG9eyav3QGxScAifHl9Omt824h//B369mTRah\nWvgEP336Abx1PoqoMM+cR8ponVCfvdnMyN8xQBD4lEq1lzBRFIlGazZaqjqzBdxkOaxoa21t5Y47\n7hj35y0tjbXCCQkJCWk2o9uRpKhUYiiKSaXiIcs+nZ02pqkwODh3bvwzAVGQMOQIhhwhSQqiEOBj\nRCX29feTqQ6StXIEBIjDbg0jLTcOR3ZQqQk2V2TH1jia7hGLafR21x7ugiDQbnSMu/0rAy/TXdnP\nL3qeJ6mmODm+jJPjy1gYWTRtuXkTwfdBFA98v4MRRI1SLkJSS+L6LnuLe9lT3E1ST9FuzCOuTT76\nNtsQBBFNq50X3/cpFgvk87m6D6phGHNCwB32Cnz++eebNY6QkJCQY44gCMyfL7N1q088rpNMiliW\ngOOUicdtbNsO/ROnEQERQzFoNdK0Gmn8wKPslMjZeQYrA5SsIjVrLhVN0seMwiVbHXZusxAFnXRH\nhWJeYaBfZOP6Vv7lH1Zy1nl9nH724Lhj+N2OC3g3t4mthS1k7QwvD7zIywMv8oXlf0SrPvl866PB\ncwW2b4mz4c0Wdm6Lc8uX19e/38HCLfAtki01T1hZlEloCYIgoOKUebe6EUVQmBfpJKUTe59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+WGGy4mmUzWfRx1W+kbN24E4OT+9ENDQ+zdu5drr70WgC1btvBnf/ZnpFIpEglJ40IIIaoURcHv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\ngg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x271690e8cc90>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "param_samples = samples[:-1]\n",
        "unconstrained_rate_samples = samples[-1][..., 0]\n",
        "rate_samples = positive_bijector.forward(unconstrained_rate_samples)\n",
        "\n",
        "plt.figure(figsize=(10, 4))\n",
        "mean_lower, mean_upper = np.percentile(rate_samples, [10, 90], axis=0)\n",
        "pred_lower, pred_upper = np.percentile(np.random.poisson(rate_samples), \n",
        "                                       [10, 90], axis=0)\n",
        "\n",
        "_ = plt.plot(observed_counts, color=\"blue\", ls='--', marker='o', label='observed', alpha=0.7)\n",
        "_ = plt.plot(np.mean(rate_samples, axis=0), label='rate', color=\"green\", ls='dashed', lw=2, alpha=0.7)\n",
        "_ = plt.fill_between(np.arange(0, 30), mean_lower, mean_upper, color='green', alpha=0.2)\n",
        "_ = plt.fill_between(np.arange(0, 30), pred_lower, pred_upper, color='grey', label='counts', alpha=0.2)\n",
        "plt.xlabel(\"Day\")\n",
        "plt.ylabel(\"Daily Sample Size\")\n",
        "plt.title(\"Posterior Mean\")\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GuBYar27YZf6"
      },
      "source": [
        "## Forecasting\n",
        "\n",
        "To forecast the observed counts, we'll use the standard STS tools to build a forecast distribution over the latent rates (in unconstrained space, again since STS is designed to model real-valued data), then pass the sampled forecasts through a Poisson observation model:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "v1HuVuk6Qocm"
      },
      "outputs": [],
      "source": [
        "def sample_forecasted_counts(sts_model, posterior_latent_rates,\n",
        "                             posterior_params, num_steps_forecast,\n",
        "                             num_sampled_forecasts):\n",
        "\n",
        "  # Forecast the future latent unconstrained rates, given the inferred latent\n",
        "  # unconstrained rates and parameters.\n",
        "  unconstrained_rates_forecast_dist = tfp.sts.forecast(sts_model,\n",
        "    observed_time_series=unconstrained_rate_samples,\n",
        "    parameter_samples=posterior_params,\n",
        "    num_steps_forecast=num_steps_forecast)\n",
        "\n",
        "  # Transform the forecast to positive-valued Poisson rates.\n",
        "  rates_forecast_dist = tfd.TransformedDistribution(\n",
        "      unconstrained_rates_forecast_dist,\n",
        "      positive_bijector)\n",
        "\n",
        "  # Sample from the forecast model following the chain rule:\n",
        "  # P(counts) = P(counts | latent_rates)P(latent_rates)\n",
        "  sampled_latent_rates = rates_forecast_dist.sample(num_sampled_forecasts)\n",
        "  sampled_forecast_counts = tfd.Poisson(rate=sampled_latent_rates).sample()\n",
        "\n",
        "  return sampled_forecast_counts, sampled_latent_rates\n",
        "\n",
        "forecast_samples, rate_samples = sample_forecasted_counts(\n",
        "   sts_model,\n",
        "   posterior_latent_rates=unconstrained_rate_samples,\n",
        "   posterior_params=param_samples,\n",
        "   # Days to forecast:\n",
        "   num_steps_forecast=30,\n",
        "   num_sampled_forecasts=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MyPFQzV8SOSs"
      },
      "outputs": [],
      "source": [
        "forecast_samples = np.squeeze(forecast_samples)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iD_kLwF1V3m-"
      },
      "outputs": [],
      "source": [
        "def plot_forecast_helper(data, forecast_samples, CI=90):\n",
        "  \"\"\"Plot the observed time series alongside the forecast.\"\"\"\n",
        "  plt.figure(figsize=(10, 4))\n",
        "  forecast_median = np.median(forecast_samples, axis=0)\n",
        "\n",
        "  num_steps = len(data)\n",
        "  num_steps_forecast = forecast_median.shape[-1]\n",
        "\n",
        "  plt.plot(np.arange(num_steps), data, lw=2, color='blue', linestyle='--', marker='o',\n",
        "           label='Observed Data', alpha=0.7)\n",
        "\n",
        "  forecast_steps = np.arange(num_steps, num_steps+num_steps_forecast)\n",
        "\n",
        "  CI_interval = [(100 - CI)/2, 100 - (100 - CI)/2]\n",
        "  lower, upper = np.percentile(forecast_samples, CI_interval, axis=0)\n",
        "\n",
        "  plt.plot(forecast_steps, forecast_median, lw=2, ls='--', marker='o', color='orange',\n",
        "           label=str(CI) + '% Forecast Interval', alpha=0.7)\n",
        "  plt.fill_between(forecast_steps,\n",
        "                   lower,\n",
        "                   upper, color='orange', alpha=0.2)\n",
        "\n",
        "  plt.xlim([0, num_steps+num_steps_forecast])\n",
        "  ymin, ymax = min(np.min(forecast_samples), np.min(data)), max(np.max(forecast_samples), np.max(data))\n",
        "  yrange = ymax-ymin\n",
        "  plt.title(\"{}\".format('Observed time series with ' + str(num_steps_forecast) + ' Day Forecast'))\n",
        "  plt.xlabel('Day')\n",
        "  plt.ylabel('Daily Sample Size')\n",
        "  plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IyUp4NnzWOcs"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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44j9ZsuS9AoMgN3v00X44OjpiZ2eHpmm0bt2GiIgpVj+rLW3fvoUWLVpZzl39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\nEEKIDCBJmxBCCCFEBpCkTQghhBAiA/z/AoluqsER5UAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x2716a95983d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_forecast_helper(observed_counts, forecast_samples, CI=80)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QmS-ybPM903-"
      },
      "source": [
        "## VI inference\n",
        "\n",
        "Variational inference can be problematic when inferring a full time series, like our approximate counts (as opposed to just\n",
        "the *parameters* of a time series, as in standard STS models). The standard assumption that variables have independent posteriors is quite wrong, since each timestep is correlated with its neighbors, which can lead to underestimating uncertainty. For this reason, HMC may be a better choice for approximate inference over full time series. However, VI can be quite a bit faster, and may be useful for model prototyping or in cases where its performance can be empirically shown to be 'good enough'.\n",
        "\n",
        "To fit our model with VI, we simply build and optimize a surrogate posterior:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7aZQEnTThgMT"
      },
      "outputs": [],
      "source": [
        "surrogate_posterior = tfp.experimental.vi.build_factored_surrogate_posterior(\n",
        "    event_shape=model.event_shape[:-1],  # Infer everything but the observed counts.\n",
        "    constraining_bijectors=constraining_bijectors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "65cf0_EiimGq"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Inference ran in 10.18s.\n"
          ]
        }
      ],
      "source": [
        "# Allow external control of optimization to reduce test runtimes.\n",
        "num_variational_steps = 200 # @param { isTemplate: true}\n",
        "num_variational_steps = int(num_variational_steps)\n",
        "\n",
        "t0 = time.time()\n",
        "losses = tfp.vi.fit_surrogate_posterior(target_log_prob_fn,\n",
        "                                        surrogate_posterior,\n",
        "                                        optimizer=tf.optimizers.Adam(0.1),\n",
        "                                        num_steps=num_variational_steps)\n",
        "t1 = time.time()\n",
        "print(\"Inference ran in {:.2f}s.\".format(t1-t0))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zX8WtcLmk2mj"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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QoRETacXjiqTkjIw0hBBiICZkaEDXaOPEGV+v82cJIYTo3YQNjctSnPjOdVDb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\nTexR5fBynEwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x2716acdafd10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(losses)\n",
        "plt.title(\"Variational loss\")\n",
        "_ = plt.xlabel(\"Steps\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kQoUExeBkpC0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x2716ffae30d0>"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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NzARMQRAEoXNkZGSwYMHpvPHGe1RW6mRlSVxySfzTX9p7vs1m45577mf+/Llomhb7uqKi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\nfwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x27169023ef10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "posterior_samples = surrogate_posterior.sample(50)\n",
        "param_samples = posterior_samples[:-1]\n",
        "unconstrained_rate_samples = posterior_samples[-1][..., 0]\n",
        "rate_samples = positive_bijector.forward(unconstrained_rate_samples)\n",
        "\n",
        "plt.figure(figsize=(10, 4))\n",
        "mean_lower, mean_upper = np.percentile(rate_samples, [10, 90], axis=0)\n",
        "pred_lower, pred_upper = np.percentile(\n",
        "    np.random.poisson(rate_samples), [10, 90], axis=0)\n",
        "\n",
        "_ = plt.plot(observed_counts, color='blue', ls='--', marker='o',\n",
        "             label='observed', alpha=0.7)\n",
        "_ = plt.plot(np.mean(rate_samples, axis=0), label='rate', color='green',\n",
        "             ls='dashed', lw=2, alpha=0.7)\n",
        "_ = plt.fill_between(\n",
        "    np.arange(0, 30), mean_lower, mean_upper, color='green', alpha=0.2)\n",
        "_ = plt.fill_between(np.arange(0, 30), pred_lower, pred_upper, color='grey',\n",
        "    label='counts', alpha=0.2)\n",
        "plt.xlabel('Day')\n",
        "plt.ylabel('Daily Sample Size')\n",
        "plt.title('Posterior Mean')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0aoMoQyf_fWC"
      },
      "outputs": [],
      "source": [
        "forecast_samples, rate_samples = sample_forecasted_counts(\n",
        "   sts_model,\n",
        "   posterior_latent_rates=unconstrained_rate_samples,\n",
        "   posterior_params=param_samples,\n",
        "   # Days to forecast:\n",
        "   num_steps_forecast=30,\n",
        "   num_sampled_forecasts=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eQ7zJpEr_hHU"
      },
      "outputs": [],
      "source": [
        "forecast_samples = np.squeeze(forecast_samples)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lcEpkAEi_jcn"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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44j9ZsuS9AoMgN3v00X44OjpiZ2eHpmm0bt2GiIgpVj+rLW3fvoUWLVpZzl39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\nf5bEh19md2HkAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x271684d9a050>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_forecast_helper(observed_counts, forecast_samples, CI=80)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "STS_approximate_inference_for_models_with_non_Gaussian_observations.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
